Fe2o3 (molar mass = 159.7 g/mol) reacts with co (molar mass = 28.0 g/mol) according to the equation fe2o3(s) + 3 co(g) → 3 co2(g) + 2 fe(s). when 352 g fe2o3 reacts with excess co, how much fe (iron) is produced? 1. 4.41 mol fe 2. 0.907 mol fe 3. 147 g fe 4. 25.1 mol fe

Answers

Answer 1
the balanced equation for the above reaction is as follows
Fe₂O₃ + 3CO ---> 3CO₂ + 2Fe
Fe₂O₃ reacts with excess CO, which makes Fe₂O₃ the limiting reactant. the amount of products formed depends on the amount of limiting reactant present.
Number of moles of Fe₂O₃ reacted - 352 g / 159.7 g/mol = 2.204 mol
stoichiometry of Fe₂O₃ to Fe is 1:2
number of Fe moles formed - 2 x 2.20 mol = 4.408 mol
therefore number of Fe moles formed - 4.41 mol
answer is 1. 4.41 mol Fe

Answer 2

When 352 g of Fe₂O₃ reacts with excess CO, it produces 4.41 mol of Fe.

To determine how much Fe (iron) is produced when 352 g of Fe₂O₃ reacts with excess CO, follow these steps:

Calculate moles of Fe₂O₃:

The molar mass of Fe₂O₃ is 159.7 g/mol.

Moles of Fe₂O₃ = 352 g / 159.7 g/mol = 2.20 mol Fe₂O₃.

Determine the mole ratio of Fe₂O₃ to Fe using the balanced equation:

The balanced equation is Fe₂O₃ + 3CO → 3CO₂ + 2Fe.

1 mol of Fe₂O₃ produces 2 mol of Fe.

Calculate moles of Fe produced:

Moles of Fe = 2.20 mol Fe₂O₃ * 2 mol Fe / 1 mol Fe₂O₃ = 4.40 mol Fe.

Convert moles of Fe to grams:

The molar mass of Fe is 55.85 g/mol.

Mass of Fe = 4.40 mol * 55.85 g/mol = 245.74 g of Fe.

The correct answer is option 1: 4.41 mol Fe.


Related Questions

if you have 100 grams of S8, how many moles of S8 is that

Answers

Given mass= m =100 g
Molar mass= M = (32.06 * 8)= 256.48 g/mol
No. of moles= n=?

n= Given mass/ Molar mass
n= 100/256.48
n=0.38989 mol

How many carbon-carbon sigma bonds are present in each of the following molecules: benzene, cyclobutane?

Answers

The first bond which forms between two atoms is known as Sigma Bond. It is considered as the strongest covalent bond which forms by the head-on overlapping between two orbitals.

In Benzene there are six sp² hybridized carbon atoms. Each carbon atom is bonded to two carbons atoms and one hydrogen atom. Each carbon atom is bonded to one carbon atom via a double bond and through single bond to another carbon atom. Hence, there are Six sigma bonds between carbon atoms in Benzene.

In Cyclobutane there are four sp³ hybridized carbon atoms. Each carbon atom is singly bonded to two other carbon atoms and two hydrogen atoms. Therefore, there are FOUR sigma bonds between the carbon atoms of cyclobutane.

The sigma bonds are highlighted BLUE in given structures,

Final answer:

Benzene has six carbon-carbon sigma bonds because each carbon atom forms two sigma bonds with its adjacent carbon atoms. Cyclobutane has four carbon-carbon sigma bonds since it is a four-membered ring with each carbon bonded to two other carbons.

Explanation:

The question asks about the number of carbon-carbon sigma bonds in benzene and cyclobutane. Let's examine each molecule separately.

Benzene (C₆H₆)

In benzene, the carbons form a hexagonal ring and each carbon atom is bonded to two other carbon atoms. The structure of benzene is often depicted with alternating single and double bonds. However, due to resonance, the electrons are delocalized and each carbon-carbon bond is equivalent, resembling a structure with one-and-a-half bonds. Despite the presence of alternating double bonds, each carbon is involved in two sigma bonds with adjacent carbons and one sigma bond with a hydrogen atom, making a total of six carbon-carbon sigma bonds in benzene.

Cyclobutane (C₄H₈)

Cyclobutane is a four-membered ring where each carbon atom is bonded to two other carbons forming single bonds. Thus, for cyclobutane, there are four carbon-carbon sigma bonds, one between each pair of adjacent carbon atoms.

Find the new concentration of a solution if 25.0 mL of water is added to 125.0 mL of 0.150 M NaCl solution. What is the final volume? mL

Answers

Answer:

150.0 is the final volume

next question is a

and the next is 0.125 M

Explanation:

got it right in edge in 2020

Final answer:

To calculate the new concentration of NaCl solution after dilution, the final volume of the solution is determined to be 150.0 mL by adding the initial volume and the volume of water added. Using the molarity equation, the new concentration is found to be 0.125 M.

Explanation:

To find the new concentration of the NaCl solution after dilution, we use the concept of molarity and the principle of conservation of mass. The amount of solute (NaCl in this case) stays the same, but the volume increases when more solvent (water) is added.

The initial molarity (Mi) of the NaCl solution is 0.150 M and the initial volume (Vi) is 125.0 mL. The volume of water added is 25.0 mL.

The final volume (Vf) is the sum of the initial volume and the volume of water added:

Vf = Vi + volume of water added

Vf = 125.0 mL + 25.0 mL

Vf = 150.0 mL

The new concentration Cf can be calculated using the formula:

Ci × Vi = Cf × Vf

(0.150 M) × (125.0 mL) = Cf × (150.0 mL)

Cf = (0.150 M × 125.0 mL) / 150.0 mL

Cf = 0.125 M

The final volume of the solution is 150.0 mL.

Why are Noble gases inert?
A. They cannot form bonds because they have 0 electrons in their valence shell.
B. They are actually so reactive that they bond instantly with any substance they touch. This means they cannot be found in their pure form in nature.
C. They have a full shell of valence electrons.
D. They bond only with atoms of their own element.

Answers

Correct answer is C. They have a full shell of valence electrons. 

Carl crumbled a piece of paper before throwing it in the trash can. Which is true about the paper after it has been crumbled

Answers

Answer is C: It's appearance changed.

Final answer:

Crumpling a piece of paper doesn't change its mass but alters its shape, leading to reduced air resistance.

Explanation:

When Carl crumbled a piece of paper before throwing it in the trash can, the physical shape of the paper changed, but not its mass. This action relates to a physics concept concerning gravity and air resistance.

An important observation is that when different objects are dropped from the same height, like a crumpled piece of paper and a textbook, they will hit the ground at approximately the same time if we ignore air resistance.

This is because all objects in a vacuum fall at the same rate regardless of mass, due to the uniform acceleration caused by gravity. In real-life conditions, air resistance affects how objects fall.

Crumpling the paper reduces its surface area, thereby reducing air resistance and allowing it to fall faster compared to an uncrumpled sheet of paper.

If you crumple one piece of paper into a small ball and then crumple two pieces of paper, making a bigger ball but with double the mass, they will still hit the ground at the same time if dropped from the same height because the acceleration due to gravity is constant.

The solubility product for chromium(iii) fluoride is ksp = 6.6 × 10–11. what is the molar solubility of chromium(iii) fluoride?

Answers

Final answer:

To determine the molar solubility of chromium(III) fluoride, we need to use the solubility product constant (Ksp) of 6.6 × 10⁻¹¹. The molar solubility of chromium(III) fluoride is 8.184 × 10⁻⁴M.

Explanation:

To determine the molar solubility of chromium(III) fluoride, we need to use the solubility product constant (Ksp) of 6.6 × 10⁻¹¹ for chromium(III) fluoride. The Ksp expression is Ksp = [Cr³⁺][F⁻]³.

Let's assume the molar solubility of chromium(III) fluoride is x M. Since the stoichiometry of the balanced equation for its dissolution is 1:3 (one chromium ion per three fluoride ions), the equilibrium expression becomes Ksp = x(3x)³.

Now, we can set up the expression and calculate the molar solubility by solving the equation: Ksp = 108x⁴ = 6.6 × 10⁻¹¹. Solving for x gives x = 8.184 × 10⁻⁴ M. Therefore, the molar solubility of chromium(III) fluoride is 8.184 × 10⁻⁴ M.

n comparison to molecules that interact by London dispersion forces only, the melting point of similar-sized molecules forming hydrogen bonds would most likely be about the same. unpredictable. lower. higher.

Answers

Hydrogen bonds are the strongest intermolecular bonds, so the melting points would be much higher. 

Answer:

d

Explanation:

Given the starting solution had a concentration of 1.25 m, how many moles of co[h2o]6cl2 were available in the amount of starting solution you used

Answers

Final answer:

To calculate the number of moles of co[h2o]6cl2 in the starting solution, we can use the molarity (concentration) of the solution and the volume of the solution used. If 1L of the solution is used, the number of moles would be equal to the molarity of the solution.

Explanation:

The question is about finding out the number of moles of co[h2o]6cl2 present in a starting solution with a given molarity (concentration). Molarity, in a nutshell, is defined as the number of moles of solute per liter of solution. Given that the molarity of the solution is 1.25M, we can directly relate this to the number of moles using the definition of molarity. For example, if we used 1L of the solution, the number of moles would be 1.25moles. If less or more than 1L of solution was used, the number of moles would be less or more, respectively, which is directly proportional to the volume of the solution used.

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A stock solution of naoh is 0.800 m. what volume of this solution (in ml) is needed to prepare 2.00 l of 0.342 m naoh?

Answers

The  volume  of  the solution(in Ml)  needed  to  prepare 2.00 L  of 0.342 M  NaOH    is calculated using the below  formula

M1V1 =M2V2
M1=0.800 M
V1=?
M2=0.342  m
V2=  2.00  L

by  making  V1   the  subject  of the  formula = M2V2/M1

= 2.00 L x 0.342/ 0.800 =0.855  L  stock  solution  is neede


Define atom. list the subatomic particles, describe their relative masses,charges, and positions in the atom.

Answers

atom is a small indivisible particle that can only be seen under a microscope

Given that delta hvap is 58.2 kj/mol and the boiling point is 83.4 c 1atm if one mole of this substance is vaporized at 1atm calculate delta ssurr

Answers

Change in Gibb's free energy of system (ΔG) = ΔH - TΔS.........(Eq. 1)
Now, if magnitude of ΔG <0, then reaction is spontaneous.
         if magnitude of ΔG > 0, then reaction is non-spontaneous. 
         At equilibrium, ΔG = 0
When at boiling point, liquid state is in equilibrium with vapour state. Hence, it present case ΔG = 0

∴ Eq 1 becomes, ΔH = TΔS
here, ΔH = 58.2 kj/mol (Given),
∴ At T = 83.4 oC = 356.4 K, ΔS = 0.1633 kj/mol.K

In this lab, you will use the flame test to identify the metal ion in two boxes of unidentified fireworks. Write an investigative question that you can answer by doing this experiment.

Answers

The first one is chlorine ion, the second one is metal ion.

The concentration of the solid phase _____ the quantity present.

depends on
changes with the amount of
is equal to
always remains the same regardless of

Answers

The concentration of the solid phase always remains the same regardless of the quantity present. Most of the chemical reactions and separation systems involve the transport of more or one components in solid phase.
For example, in the process of solid catalyzed reactions, the result of solid phase transport might be negligible though it is hard to identify it in the rate of data in the analysis.

Answer: Option (b) is the correct answer.

Explanation:

A solution that contains more number of solute particles than the solvent particles is known as a concentrated solution.

For example, concentrated solution of sulfuric acid.

On the other hand, a solution that contains less number of solute particles than the solvent particles is known as a dilute solution.

For example, a dilute solution of HCl.

Hence, we can conclude that concentration of a substance changes with change in the amount of solute.

Therefore, the concentration of the solid phase changes with the amount of the quantity present.

Among the alkali earth metals, the tendency to react with other substances

A) increases from bottom to top within the group.

B) is shown by the ways they react with water.

C) varies in an unpredictable way within the group.

D) does not vary among the members of the group.

Answers

The answer would be letter A.Among the alkali earth metals, the tendency to react with other substances increases from bottom to top within the group. We know that when there is an increase of metallic property, there will also be an increase of reactivity. 

The reaction of cr2+(aq) with cr2o2−7(aq) in acid solution to form cr3+(aq). calculate δg∘rxn.

Answers

The reaction is:
6 Cr²⁺ + Cr₂O₇²⁻ + 14 H⁺ → 8 Cr³⁺ + 7 H₂O

E₀ = 1.33 - (-0.5) = 1.83 V

ΔG = - n f E₀
      = - 6 * 96485  * 1.83
      = - 1059405.3 J / mol
      = - 1059.4 kJ / mol

Answer:

The correct answer is -1059.45 kJ.

Explanation:

The balanced equation is:

6Cr₂⁺ + Cr₂O₇²⁻ + 14H⁺ ⇒ 8Cr₃⁺ + 7H₂O

In the mentioned reaction 6 electrons are transferred

By calculating Ecell with the use of reduction potential of each cell:

Ecell = Eox + Ered

Ered = 0.50V

Eox = -Ered = -(-0.50V) = 0.50V

Ered = 1.33V

Ecell = 0.50V + 1.33V

Ecell = 1.83V

Now in order to calculate ΔG

n = 6, Faraday constant (f) = 9.68470 × 10⁴ = 96847 C mol⁻¹

ΔG = -nFE

ΔG = -6 × 96487 C mol-1 × 1.83V

ΔG = -1059.42 KJ

The relation between ΔG and ΔG°rxn

ΔG = ΔG° + RTlnQ

Under the standard condition Q = 1 and ΔG = ΔG°

Thus,

ΔG°rxn = ΔG = -1059.42 KJ

what is the volume of 12.0 g of cl2 gas at stp

Answers

Hi I think I might know the answer to your question it is pretty tricky though!
Chlorine Gas = 70.8 grams/moles
Moles of Chlorine Gas = 57.8/70.8 = 0.816 mol
Volume Gas at STP = 22.4 L/mol
Volume of Chlorine Gas = .816*22.4=18.22 Litters
I hoped that helps if not so sorry!

Answer:

[tex]V=3.79L[/tex]

Explanation:

Hello,

In this case, we are talking about an ideal gas problem in which 12.0 g of chlorine gas is at standard both pressure (1atm) and temperature (0°C), therefore, to compute the corresponding volume, one applies the ideal gas law, then converts from grams to moles considering the diatomic chlorine and subsequently solves for volume as shown below:

[tex]PV=nRT\\V=\frac{nRT}{P}=\frac{12.0gCl_2*\frac{1molCl_2}{70.9gCl_2} *0.082 \frac{atm*L}{mol*K} * 273.15K}{1atm}  \\V=3.79L[/tex]

Best regards.

Calculate the freezing point of a 0.08500 m aqueous solution of nano3. the molal freezing-point-depression constant of water is 1.86°c/m. remember to include the value of i.

Answers

Depression in freezing point (Δ[tex] T_{f} [/tex]) = [tex] K_{f} [/tex]×m×i,
where, [tex] K_{f} [/tex] = cryoscopic constant = [tex] 1.86^{0} C/m[/tex],
m= molality of solution = 0.0085 m
i = van't Hoff factor = 2 (For [tex] NaNO_{3} [/tex])

Thus, (Δ[tex] T_{f} [/tex]) = 1.86 X 0.0085 X 2 = [tex] 0.03162^{0}C [/tex]

Now, (Δ[tex] T_{f} [/tex]) = [tex] T^{0} [/tex] - T
Here, T = freezing point of solution
[tex] T^{0} [/tex] = freezing point of solvent = [tex] 0^{0}C [/tex]
Thus, T = [tex] T^{0} [/tex] - (Δ[tex] T_{f} [/tex]) = -[tex] 0.03162^{0}C [/tex]

Answer : The freezing point of a solution is, [tex]0.32^oC[/tex]

Explanation :

First we have to calculate the Van't Hoff factor (i) for [tex]NaNO_3[/tex].

The dissociation of [tex]NaNO_3[/tex] will be,

[tex]NaNO_3\rightarrow Na^++NO_3^-[/tex]

So, Van't Hoff factor = Number of solute particles = [tex]Na^++NO_3^-[/tex] = 1 + 1 = 2

Now we have to calculate the freezing point of a solution.

Formula used for lowering in freezing point :

[tex]\Delta T_f=i\times k_f\times m[/tex]

or,

[tex]T_f^o-T_f=i\times k_f\times m[/tex]

where,

[tex]\Delta T_f[/tex] = change in freezing point

[tex]T_f[/tex] = temperature of solution = ?

[tex]T^o_f[/tex] = temperature of pure water = [tex]0^oC[/tex]

[tex]k_f[/tex] = freezing point constant  = [tex]1.86^oC/m[/tex]

m = molality  = 0.08500 m

i = Van't Hoff factor = 2

Now put all the given values in this formula, we get the freezing point of a solution.

[tex]0^oC-T_f=2\times (1.86^oC/m)\times 0.08500m[/tex]

[tex]T_f=0.32^oC[/tex]

Therefore, the freezing point of a solution is, [tex]0.32^oC[/tex]

In the lewis structure of ch3oh, how many bonding pairs of electrons are there?

Answers

Answer:
            There are five bonding pairs of electrons in Methanol.

Explanation:
                   Those electron pairs which are being shared between two atoms in molecule are called as bonding pair electrons. While, those electron pairs which are not involved in bond formation and are not shared between two atoms are called as Non-Bonding electron pairs.
                   In molecule of Methanol as shown below, it can be seen that carbon atom is forming four bonds with three hydrogen atoms and one oxygen atom by sharing four electron pairs and oxygen is forming two bonds, one with carbon atom and one with hydrogen atom. There are two lone pair of electrons present on oxygen atom which are not taking part in and formation.

the number of atoms bonded to the central atom is 4

Explanation:

which of the following is a balanced chemical equation for the reaction of magnesium with nitrogen gas to form magnesium nitride

Answers

So the unbalanced equation would be Mg + N^2 --> Mg^3N^2

Which means the balanced equation would be 3Mg + N^2 --> Mg^3N^2

This is balance the equation out since you now has 3 magnesium and 2 nitrogen on the left side, and 3 magnesium on 2 nitrogen on the right. Double check my work though, it's been awhile.

Question 7 what is the volume of 28.0 g of nitrogen gas at stp? 44.8 l 33.6 l 11.2 l 22.4 l none of the above

Answers

At STP, 1 mol of gas corresponds to 22.4 L. The molar mass of nitrogen is 14.0g so the molar mass of nitrogen gas (N2) is 28.0g. The moles of nitrogen in this sample of nitrogen gas is
                           28.0 g / (1 mol / 28.0 g) = 1.00 mol
If we convert to liters, we get
                           (1.00 mol)(22.4 L / 1mol) = 22.4 L
Therefore, your answer is 22.4 L.

The increase in the population of people living in urban areas will cause a decrease in urban sprawl.


Please select the best answer from the choices provided

T
F

Answers

This is false/ i know because i live in an urban area and it increases by human construction.

Answer: The given statement is false.

Explanation:

When there occurs unrestricted growth and development in number of urban areas for housing, commercial development, roads etc then it is known as urban sprawl.

Hence, when there will be more population in an urban area then there will be more urban sprawl because then there will be more demand for facilities.

Thus, we can conclude that the statement increase in the population of people living in urban areas will cause a decrease in urban sprawl, is false.

what is the molarity of 10.0 g of kcl in 0.500 l of solution

Answers

Molarity is defined as number of moles of the solute in 1 liter of solution.

Molarity = Moles of solute (mol) / Volume of the solution (L)

moles of KCl = mass (g) / molar mass (g/mol)
                      = 10.0 g / 74.5 g/mol
                      = 0.134 mol

Hence molarity = 0.134 mol / 0.500 L
                         = 0.268 mol/L

The equilibrium constant for the reaction sr(s) + mg2+(aq) ⇌ sr2+(aq) + mg(s) is 3.69 × 1017 at 25°c. calculate e o for a cell made up of sr / sr2+ and mg / mg2+ half-cells.

Answers

we are going to use this formula:

E° = 0.0592/ n * ㏒K

when E° is the standard state cell potential

and n is number of moles of electrons transferred in the balanced equation

for the reaction of the cell.

Sr(s) + Mg2+ (aq) ↔ Sr2+(aq) + Mg(s)

we can get it by using the given balanced equation, we here have 2 electrons

transferred so, n = 2 

and K the equilibrium constant = 3.69 x 10^17

so, by substitution:

∴ E° = 0.0592 / 2 * ㏒ (3.69 x 10^17)

        = 0.52 V

To calculate the standard electrode potential (E°) for a cell composed of Sr/Sr²⁺ and Mg/Mg²⁺ half-cells, use the Nernst equation with the given equilibrium constant value. The resulting E° is approximately 1.038 V.

To find the standard electrode potential (E°) for the cell, we can use the Nernst equation and the relationship between the equilibrium constant (Keq) and the standard electrode potential:

Nernst equation:

E° = (RT / nF) * ln(Keq)

Where:

R = 8.314 J/(mol·K)T = 298 K (since the temperature is 25°C)n = 2 (number of electrons transferred, as each Sr replaces an Mg)F = 96485 C/mol

Plugging in the values, we get:

E° = (8.314 * 298 / (2 * 96485)) * ln(3.69 × 1017)

Simplify the constants:

E° = (0.0257 V) * ln(3.69 × 1017)

Evaluating the natural logarithm:

E° = 0.0257 * 40.38

E° ≈ 1.038 V

Therefore, the standard electrode potential (E°) for the cell is approximately 1.038 V.

Sucrose is very soluble in water. at 25◦c, 211.4 grams of sucrose will dissolve in 100 g of water. given that the density of the saturated sucrose solution is 1.34 g/ml, what is the molarity of the solution

Answers

Final answer:

The molarity of the sucrose solution is calculated by finding the number of moles of sucrose and the volume of the solution in liters. By using the provided data, we came up with a molarity of 2.67 M.

Explanation:

To calculate the molarity of the solution, we need to know the number of moles of sucrose and the volume of the solution in liters. Given that the molecular weight of sucrose (C12H22O11) is approximately 342 g/mol, the number of moles of sucrose in 211.4 g can be calculated as (211.4 g) / (342 g/mol) = 0.618 moles.

To get the volume of the solution, first calculate the total mass of the solution which is mass of water + mass of sucrose = 100 g + 211.4 g = 311.4 g. Since the density of the solution is provided as 1.34 g/ml, convert this to kg/L to get the volume. So, 311.4 g / 1.34 g/ml = 232.39 ml or 0.232 L.

Finally, we calculate the molarity which is moles/volume in liters. So, molarity = 0.618 moles / 0.232 L = 2.67 M.

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Answer:

2.66 M

from ut quest

Find the age t of a sample, if the total mass of carbon in the sample is mc, the activity of the sample is a, the current ratio of the mass of 14 6c to the total mass of carbon in the atmosphere is r, and the decay constant of 14 6c is λ. assume that, at any time, 14 6c is a negligible fraction of the total mass of carbon and that the measured activity of the sample is purely due to 14 6c. also assume that the ratio of mass of 14 6c to total carbon mass in the atmosphere (the source of the carbon in the sample) is the same at present and on the day when the number of 14 6c atoms in the sample was set. express your answer in terms of the mass ma of a 14 6c atom, mc, a, r, and λ.

Answers

the age of the sample (t) can be expressed as:** t = (1 / λ) * ln(a / r)

**1. Relate Activity and Initial Abundance:**

The activity (a) of the sample is proportional to the current number of ¹⁴⁶C atoms in the sample (N) relative to the initial number of ¹⁴⁶C atoms (N₀) at the time the sample was isolated from the atmosphere:

a ∝ N / N₀

**2. Relate Number of Atoms to Mass:**

The number of ¹⁴⁶C atoms (N) is related to the total mass of carbon (mc) and the mass of a single ¹⁴⁶C atom (ma) through Avogadro's constant (Na):

N = (mc / ma) * Na

**3. Consider Decay and Substitute:**

Over time, ¹⁴⁶C atoms decay with a decay constant (λ). We can express the change in the number of ¹⁴⁶C atoms using the radioactive decay equation:

dN/dt = -λN

Since we're looking for the age (t), we can integrate this equation to find the relationship between N and t:

N(t) = N₀ * e^(-λt)  // (Equation 1)

Substitute N₀ with the initial number of ¹⁴⁶C atoms proportional to the initial ¹⁴⁶C/¹²C ratio in the atmosphere (r * mc / ma * Na):

N(t) = (r * mc / ma * Na) * e^(-λt) // (Equation 2)

**4. Relate Activity and Current ¹⁴⁶C/¹²C Ratio:**

The current activity (a) is also proportional to the current ¹⁴⁶C/¹²C ratio in the sample:

a ∝ (mc / ma * Na) * [N(t) / mc]

Substitute N(t) from Equation 2:

a ∝ (mc / ma * Na) * [ (r * mc / ma * Na) * e^(-λt) ] / mc

**5. Solve for Age (t):**

Cancel common factors and simplify:

a ∝ r * e^(-λt)

Taking the natural logarithm of both sides:

ln(a/r) = -λt

The final expression for the age of the sample [tex]t[/tex] in terms of the given variables is [tex]t = -\frac{1}{\lambda} \ln \left( \frac{a}{\lambda \cdot \frac{m_c \cdot r}{m_a}} \right)[/tex]

Step 1: Understanding Activity

The activity [tex]A[/tex] of a radioactive sample is related to the number of radioactive nuclei present [tex]N[/tex] by the equation:
[tex]A = \lambda N[/tex]
Here, [tex]\lambda[/tex] is the decay constant and represents the probability of decay per unit time.

Step 2: Relating Activity to Carbon-14

Given that the measured activity [tex]a[/tex] of the sample is purely due to [tex]^{14}C[/tex] and can be expressed as:
[tex]a = \lambda N_t[/tex]
Where [tex]N_t[/tex] is the current number of [tex]^{14}C[/tex] atoms in the sample.

Step 3: Finding Original Amount of Carbon-14

If we denote the original number of [tex]^{14}C[/tex] atoms in the sample as [tex]N_0[/tex], this can be related to the total mass of carbon in the sample and the ratio [tex]r[/tex] as follows:
[tex]N_0 = \frac{m_c \cdot r}{m_a}[/tex]
Where [tex]m_a[/tex] is the mass of a single [tex]^{14}C[/tex] atom.

Step 4: Calculating Age

The relationship between current [tex]N_t[/tex], original [tex]N_0[/tex], and time [tex]t[/tex] can be expressed using the formula for exponential decay:
[tex]N_t = N_0 e^{-\lambda t}[/tex]
Thus, rearranging this expression, we find:
[tex]t = -\frac{1}{\lambda} \ln \left( \frac{N_t}{N_0} \right)[/tex]

Step 5: Substituting Values

Substituting in our earlier expressions:
[tex]t = -\frac{1}{\lambda} \ln \left( \frac{N_t}{\frac{m_c \cdot r}{m_a}} \right)[/tex]
This simplifies further to:
[tex]t = -\frac{1}{\lambda} \left( \ln(N_t) - \ln\left(\frac{m_c \cdot r}{m_a}\right) \right)[/tex]
Thus, we can express [tex]t[/tex] as:
[tex]t = -\frac{1}{\lambda} \ln(N_t) + \frac{1}{\lambda} \ln\left(\frac{m_c \cdot r}{m_a}\right)[/tex]
[tex]t = -\frac{1}{\lambda} \ln \left( \frac{a}{\lambda \cdot \frac{m_c \cdot r}{m_a}} \right)[/tex]

What is the ground-state electron configuration for the element cobalt (z = 27)?

Answers

Final answer:

The ground-state electron configuration for cobalt (Z = 27) is [Ar] 3d7 4s2.

Explanation:

The ground-state electron configuration for the element cobalt (Co), which has an atomic number (Z) of 27, is as follows:

Co: [Ar] 3d74s2

This configuration indicates that cobalt has 2 electrons in the outermost 4s subshell and 7 electrons in the 3d subshell after the [Ar] noble gas core.

The ground-state electron configuration for the element cobalt (Z = 27) is 1s²2s²2p⁶3s²3p⁶4s²3d⁷. Co has 27 protons, 27 electrons, and 33 neutrons. The electron configuration represents the distribution of electrons in the energy levels and orbitals of an atom.

What crossed-aldol product results when butanal is heated in the presence of excess benzaldehyde and sodium hydroxide? draw the molecule on the canvas by choosing buttons from the tools (for bonds), atoms, and advanced template toolbars. the single bond is active by defa?

Answers

Final answer:

When butanal is heated with excess benzaldehyde and sodium hydroxide, the crossed-aldol product formed is 4-phenyl-2-butanol, which is obtained through the aldol condensation reaction.

Explanation:

Crossed-aldol product formation occurs when two different carbonyl compounds, such as aldehydes or ketones, react in an aldol condensation. The products are a mixture of different aldol adducts, resulting from the nucleophilic addition of one carbonyl compound to the other. This reaction allows for the creation of complex molecules with varied functionalities.

When butanal is heated in the presence of excess benzaldehyde and sodium hydroxide, the crossed-aldol product formed is 4-phenyl-2-butanol. The product is obtained by the aldol condensation reaction between butanal and benzaldehyde. In this reaction, a molecule of water is eliminated, and the resulting product contains both the aldehyde and the alcohol functional groups.

Learn more about Crossed-aldol product formation here:

https://brainly.com/question/32134011

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A sound is first produced by making something BLANK . The sound then travels through a BLANK to reach the ears, which are the parts of the body that allow for sounds to be heard.

Answers

A sound is first produced by making something VIBRATE. The sound then travels through a MEDIUM to reach the ears, which are the parts of the body that allow for sounds to be heard.

A sound is first produced by making something vibrates and then the sound travels through a medium and reach our ears.

Which are the parts of the body that allow for sounds to be heard?

The ear is responsible for hearing sounds as well as for balance in the human body. The ear has three parts i.e. the outer, middle and inner ears. We hear the sound when the body starts vibration.

So we can conclude that a sound is first produced by making something vibrates and then the sound travels through a medium and reach our ears.

Learn more about sound here: https://brainly.com/question/1199084

A 3.5 gram sample of a radioactive element was formed in a 1960 explosion of an atomic bomb at Johnson Island in the Pacific test site. The half-life of the radioactive element is 28 years. How much of the original sample will remain in the year 2030? Choose the closest.

DO NOT GUESS, ONLY COMMENT IF YOU KNOW

Answers

0.50 g

That should be the correct answer :)

Answer : The correct answer for amount of radioisotope remain in 2030 is 0.619 g .

Radioactive Decay is emission of radiations ( in form of alpha , beta particle etc ) by unstable atom .

Radioactive decay is FIRST ORDER reaction . So , the equation of first order can be used to find decay constant , amount of radioisotopes or half life .

The equation for radioactive decay is given as :

[tex] ln (\frac{N}{N_0}) = -k * t [/tex]

Where : N = amount of radioisotope at time t

N₀ = amount of radioisotope initially present

k = decay constant t = time

Half life :

It is time when amount of radioisotope decrease to 50 % of its original amount . Half life [tex] (T_\frac{1}{2} ) [/tex] and decay constant can be related :

[tex] T_\frac{1}{2} = \frac{ln 2 }{k} = \frac{0.693}{k} [/tex]

Following are the steps can be used to determine amount of radioisotope (N) :

1) To find decay constant :

Given : [tex] (T_\frac{1}{2} ) [/tex] = 28 yrs

Decay constant can be calculated using half life by plugging value in half life formula :

[tex] 28 yrs = \frac{0.693}{k} [/tex]

On multiplying both side by k

[tex] 28 yrs * k= \frac{0.693}{k} *k [/tex]

On dividing both side by 28 yrs

[tex] \frac{28 yrs * k}{28 yrs} = \frac{0.693}{28 yrs} [/tex]

k = 0.02475 yrs⁻¹

2) To find amount of radioisotope (N):

Given : Amount of radioisotope originally present = 3.5 g

Time = 2030 - 1960 = 70 yrs

decay constant = 0.02475 yrs⁻¹

Amount of radioisotope (N) = ?

Plugging these values in the formula as:

[tex] ln (\frac{N}{3.5 } ) = - 0.02475 yrs^-^1 * 70 yrs [/tex]

[tex] ln (\frac{N}{3.5 } ) = - 1.7325 [/tex]

[tex] ln\frac{N}{No} [/tex] can be converted using the formula ( [tex] ln (\frac{a}{b} ) = ln a - ln b [/tex] )

ln N - ln (3.5 ) = - 1.7325

(ln 3.5 = 1.253 )

ln N -1.253 = -1.7325

Adding both side 1.253

ln N -1.253 + 1.253 = -1.7325 + 1.253

ln N = -0.4795

Taking anti ln of -0.4795

N = 0.619 g

Hence amount of radioisotope remained in 2030 is 0.619 g



How much energy does an electric hair dryer use if it draws 8.3 amps of current when using 120 volts for 5.0 minutes?

Answers

0.083kwh is the answer your welcome

Answer: The energy drawn by electric hair dryer is 2,98,800 J

Explanation:

To calculate the power of the electric hair dryer, we use the equation:

[tex]P=I\times V[/tex]

where,

P = power of electric hair dryer

I = Current of electric hair dryer = 8.3 A

V = voltage of electric hair dryer = 120 V

Putting values in above equation, we get:

[tex]P=8.3\times 120=996W[/tex]

To calculate the energy of electric hair dryer, we use the equation:

[tex]E=P\times t[/tex]

where,

E = energy of electric hair dryer = ?

P = Power of electric hair dryer = 996 W

t = time taken = 5.0 min = 300 s     (Conversion factor:  1 min = 60 sec)

Putting values in above equation, we get:

[tex]E=996\times 300=2,98,800J[/tex]

Hence, the energy drawn by electric hair dryer is 2,98,800 J

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