How many degrees of freedom does each of the following systems have? (Answer as a number, i.e., 1, 2, 3, etc.)

1. Liquid water in equilibrium with its vapor?

2. Liquid water in equilibrium with a mixture of water vapor and nitrogen?

3. A liquid solution of alcohol in water in equilibrium with its vapor?

Answer:

concentration of CrO4²⁻ ions in the final solution = 6.53 × 10⁻⁵ mol /L

Explanation:

First we calculate the number of moles of AgNO₃:

number of moles = molar concentration × volume

number of moles = 0.5 × 39.20 = 19.6 mmoles = 0,0196 moles AgNO₃

Then we calculate the number of moles of K₂CrO₄:

number of moles = mass / molar weight

number of moles = 5.832 / 194 = 0.03 moles K₂CrO₄

The chemical reaction will look like this:

2 AgNO₃ + K₂CrO₄ → Ag₂CrO₄ + 2 KNO₃

Now we devise the following reasoning:

if          2 moles of AgNO₃ are reacting with 1 mole of K₂CrO₄

then    0,0196  moles of AgNO₃ are reacting with X moles of K₂CrO₄

X = (0.0196 × 1) / 2 = 0.0098 moles of K₂CrO₄

now the the we calculate the amount of unreacted K₂CrO₄:

unreacted K₂CrO₄ = 0.03 - 0.0098 = 0.0202 moles

now the molar concentration of CrO4²⁻ ions:

molar concentration = number of moles / solution volume (L)

molar concentration = 0.0202 / (39.20 + 270) = 6.53 × 10⁻⁵ mol /L

Answer:The student should be wearing a lab coat or maybe an apron to prevent chemicals from spilling or exploding onto their clothes, I do recommend a lab coat better though because it can protect your skin better. Next, make sure while messing with chemicals you are always wearing goggles, if you are not wearing them there is a chance that after touching chemicals you could touch your eyes. And that brings me to washing your hands straight away after messing with chemicals. You could also wear gloves and just take them off when you're done but if you don't have clean hands afterward you could always put the chemicals all over your skin. But in case you do touch your eyes there is always an emergency eyewash station somewhere in the lab room. And if you are to get Chemicals on your skin, in your hair, on your clothes, or to be on fire, there shall be a shower somewhere to get rid of that. But if you read the instructions or listen closely to the teacher you shall have no problem.

Explanation:

I kinda got off topic

When a student is warming a chemical in a container using a special burner, it is very important to focus on safety by using the right safety tools.

First, the student needs to wear the right safety clothes like a lab coat, gloves, and goggles to protect themselves from getting splashed or hurt by chemicals. A lab coat stops chemicals from touching the skin, gloves keep the hands safe, and safety goggles protect the eyes from chemicals

and hot things.

Furthermore, using a fume hood is necessary to make sure there is enough fresh air circulating and to remove any dangerous fumes or gases that might be released while heating things up.

Read more about safety equipment here:

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Answer:

a) ppm

b) ppm

c) ppb

d) ppt

e) ppb

Explanation:

a) You know that 1000 g are 1 kg, and 1000 kg are 1 ton, so (1000)*(1000) g are 1 ton, so 1,000,000 grams are one ton.

b) 1000 mg are 1 g, and 1000 g are 1 liter, so 1,000,000 grams are one liter.

c) You know that 1000 ug are 1 mg, so with the b), we just need to multiply the answer by 1000, so 1,000,000,000 ug are 1 liter.

d) The same as c, 1000 ng are 1 mg. So we are talkinf of ppt.

e) 1000 mg are 1 g. And 1000 g are 1 kg, then 1000 kg are one ton. So 1,000,000,000 mg are one ton.

Answer:

2.32 m

Explanation:

So, according to definition of mole fraction:

[tex]Mole\ fraction\ of\ benzene=\frac {n_{benzene}}{n_{benzene}+n_{toluene}}[/tex]

Mole fraction = 0.176

Applying values as:

[tex]0.176=\frac {n_{benzene}}{n_{benzene}+n_{toluene}}[/tex]

[tex]0.176\times ({n_{benzene}+n_{toluene}})={n_{benzene}}[/tex]

So,

[tex]0.176\times n_{toluene}}=0.824\times {n_{benzene}}[/tex]

[tex]{n_{benzene}}=\frac {0.176}{0.824}\times n_{toluene}}[/tex]

[tex]{n_{benzene}}=0.2136\times n_{toluene}}[/tex]

Also, Molar mass of toluene = 92.14 g/mol

Thus,

The formula for the calculation of moles is shown below:

[tex]moles = \frac{Mass\ taken}{Molar\ mass}[/tex]

[tex]Mass=92.14\times n_{toluene}}\ g[/tex]

Also, 1 g = 0.001 kg

So,

[tex]Mass\ of\ toluene=0.09214\times n_{toluene}}\ kg[/tex]

Molality is defined as the moles of the solute present in 1 kg of the solvent.

It is represented by 'm'.

Thus,  

[tex]Molality\ (m)=\frac {0.2136\times n_{toluene}}{0.09214\times n_{toluene}}[/tex]

Molality of benzene = 2.32 m

Final answer:

The molality of the solution of benzene dissolved in toluene is 0.00543 mol/kg.

Explanation:

The molality of a solution can be calculated using the mole fraction and the molar mass of benzene and toluene. The mole fraction of benzene can be calculated by dividing the moles of benzene by the total moles of benzene and toluene. The moles of benzene can be determined using the given volumes of benzene and toluene and their respective densities. The molar mass of benzene is 78.11 g/mol. By substituting the values into the formula, we can calculate the molality of the solution to be 0.176 * 78.11 g/mol / (1000 g + 0.867 g/mL * 100 mL + 0.874 g/mL * 300 mL) = 0.00543 mol/kg.

Answer:

1) The density of air at 40 degrees Celsius and 3 atm pressure is 3.4 g/L.

2) Molecular mass of linanyl acetate  is 196 g/mol.

Explanation:

1) Average molecular weight of an air ,M= 28.97 g/mol

[tex]PV=nRT[/tex]

or [tex] PM=dRT[/tex]

P = Pressure of the gas

T = Temperature of the gas

d = Density of the gas

M = molar mass of the gas

R = universal gas constant

P = 3 atm, T = 40°C = 313.15 K, M = 28.97 g/mol

[tex]d=\frac{PM}{RT}=\frac{3 atm \times 28.97 g/mol}{0.0821 atm L/ mol K\times 313.15 K}[/tex]

d = 3.4 g/mL

The density of air at 40 degrees Celsius and 3 atm pressure is 3.4 g/L.

2) Molecular formula of Linanyl acetate = [tex]C_{12}H_{20}O_2[/tex]

Atomic mass sof carbon  = 12.01 g/mol

Atomic mass of hydrogen = 1.01 g/mol

Atomic mass of oxygen  = 16.00 g/mol

Molecular mass of  Linanyl acetate :

[tex]12\times 12.01 g/mol+20\times 1.01 g/mol+2\times 16.00 g/mol =196.32 g/mol \approx 196 g/mol[/tex]

Final answer:

The isotopic symbol for an isotope of iodine with 78 neutrons is 131I53. The isotopic symbol for an isotope of cesium with 82 neutrons is 137Cs55. The isotopic symbol for an isotope of strontium with 52 neutrons is 90Sr38.

Explanation:

An isotope of iodine with 78 neutrons would have an atomic number of 53. To write the isotopic symbol, we include the atomic number as a subscript and the mass number (atomic number + number of neutrons) as a superscript. Therefore, the isotopic symbol for the iodine isotope with 78 neutrons would be 131I53.

An isotope of cesium with 82 neutrons would have an atomic number of 55. So, the isotopic symbol for the cesium isotope with 82 neutrons would be 137Cs55.

An isotope of strontium with 52 neutrons would have an atomic number of 38. Hence, the isotopic symbol for the strontium isotope with 52 neutrons would be 90Sr38.

Answer:

Volumetric flow rate: Q = 1000 L/s

Explanation:

Volumetric flow rate, also called the rate of fluid flow, is described as volume of fluid that passes a particular point per unit time. The SI unit of volumetric flow rate is m³/s.  

Whereas, mass flow rate is defined as the mass of substance that passes through a point per unit of time. SI unit is kg/s.

Given- mass flow rate: ṁ = 1 kg/s and density: ρ = 1 kg/m³

Therefore, volumetric flow rate can be calculated by

[tex]Q = \frac{\dot{m}}{\rho } = \frac{1 kg/s}{1 kg/m^{3}} = 1 m^{3}/s[/tex]

Since, 1 m³/s = 1000 L/s

Therefore, volumetric flow rate: Q = 1 m³/s = 1000 L/s

Answer:

-1.06

Explanation:

0.345 has three significant figures since the zero does not represent a significant figure.

So, usign the calculator, we find ln (0.345) = -1.06421086195

Now, the problem says that you need to report your answer to three significant figures.

So, you should take the first three numbers of the answer:

ln (0.345) = -1.06

Answer :  a) 40075.14 J/mol

Explanation :

According to the Arrhenius equation,

[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]

or,

[tex]\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}][/tex]

where,

[tex]K_1[/tex] = rate constant at [tex]440K[/tex] = k

[tex]K_2[/tex] = rate constant at [tex]550K[/tex] = 10 k

[tex]Ea[/tex] = activation energy for the reaction = ?

R = gas constant = 8.314 J/mole.K

[tex]T_1[/tex] = initial temperature = 440 K

[tex]T_2[/tex] = final temperature = 550 K

Now put all the given values in this formula, we get :

[tex]\log (\frac{10k}{k})=\frac{Ea}{2.303\times 8.314J/mole.K}[\frac{1}{440K}-\frac{1}{550K}][/tex]

[tex]Ea=40075.14J/mol [/tex]

Therefore, the activation energy for the reaction is 40075.14J/mol.

Sugar is the pure substance in the list. A chemical change occurs when methane gas is burned, as the chemical composition of methane is altered.

In the list provided, the pure substance is sugar. Pure substances are materials that are composed of only one type of particle, and sugar, which is made up of sucrose, meets this criterion. In contrast, substances like sea water, air, lemonade, and milk are mixtures, as they contain more than one kind of particle.

As for the second question, a chemical change happens when the composition of a substance is altered by a chemical reaction. In this scenario, the correct option is 'occurs when methane gas is burned'. Methane's combustion is a chemical reaction that produces water and carbon dioxide, which are chemically distinct from the original methane. Other options like shredding paper, vaporizing water, dissolving salt in water, or stirring powdered lemonade into water are all physical changes, as they don't alter the chemical composition of the substances involved.

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Sugar is considered a pure substance because it maintains the same composition and properties. A chemical change occurs when methane gas is burned, resulting in different substances.

From the given list, the pure substance is sugar. A pure substance has a constant composition. All specimens of a pure substance have exactly the same makeup and properties. An example of a pure substance is table sugar, or sucrose, which consists of 42.1% carbon, 6.5% hydrogen, and 51.4% oxygen by mass. It maintains the same physical properties, such as melting point, color, and sweetness, regardless of the source from which it is isolated.

Switching to the second question, the occurrence of a chemical change is evident when methane gas is burned. A chemical change always produces one or more types of matter that differ from the matter present before the change. An instance of this is the combustion or burning of methane which results in carbon dioxide and water. These yielded substances significantly differ from the original methane, hence signifying a chemical change.

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Answer: The given isotope of tin has 50 protons and 69 neutrons.

Explanation:

Atomic number is defined as the number of protons or number of electrons that are present in neutral atom. It is represented as Z.

Atomic number = Number of protons = Number of electrons

Mass number is defined as the sum of number of protons and number of neutrons. It is represented as A.

Mass number = Number of protons + Number of neutrons

We are given:

An isotope having representation [tex]_{50}^{119}\textrm{Sn}[/tex]

Mass number of Sn = 19

Atomic number = 50

Number of neutrons = Mass number - Atomic number = 119 - 50 = 69

Hence, the given isotope of tin has 50 protons and 69 neutrons.

Answer:

The two changing properties in Charles’ law are temperature and volume.

Explanation:

Charles’ law state the presence of direct relationship between temperature and volume of the system of gas molecules at constant pressure condition. In this law, the expansion of gas has been explained with the increase of temperature.

As the temperature is increased or the system of gas molecules are heated, the gas molecules tend to expand their volume to maintain the pressure same.

So the temperature and volume are directly proportional at constant pressure. Thus the two changing properties of Charles’ law is temperature and volume. The mathematical representation of Charles’ law is

V∝T (at constant Pressure)

[tex]V=kT[/tex]

Here k is the non-zero constant and V and T are volume and temperature respectively.

Answer : The percent yield of [tex]P_2O_5[/tex] is, 30.39 %

Solution : Given,

Mass of P = 2.80 g

Molar mass of P = 31 g/mole

Molar mass of [tex]P_2O_5[/tex] = 284 g/mole

First we have to calculate the moles of P.

[tex]\text{ Moles of }P=\frac{\text{ Mass of }P}{\text{ Molar mass of }P}=\frac{2.80g}{31g/mole}=0.0903moles[/tex]

Now we have to calculate the moles of [tex]NH_3[/tex]

The balanced chemical reaction is,

[tex]4P+5O_2\rightarrow 2P_2O_5[/tex]

From the reaction, we conclude that

As, 4 mole of [tex]P[/tex] react to give 2 mole of [tex]P_2O_5[/tex]

So, 0.0903 moles of [tex]P[/tex] react to give [tex]\frac{0.0903}{4}\times 2=0.04515[/tex] moles of [tex]P_2O_5[/tex]

Now we have to calculate the mass of [tex]P_2O_5[/tex]

[tex]\text{ Mass of }P_2O_5=\text{ Moles of }P_2O_5\times \text{ Molar mass of }P_2O_5[/tex]

[tex]\text{ Mass of }P_2O_5=(0.04515moles)\times (284g/mole)=12.8g[/tex]

Theoretical yield of [tex]P_2O_5[/tex] = 12.8 g

Experimental yield of [tex]P_2O_5[/tex] = 3.89 g

Now we have to calculate the percent yield of [tex]P_2O_5[/tex]

[tex]\% \text{ yield of }P_2O_5=\frac{\text{ Experimental yield of }P_2O_5}{\text{ Theoretical yield of }P_2O_5}\times 100[/tex]

[tex]\% \text{ yield of }P_2O_5=\frac{3.89g}{12.8g}\times 100=30.39\%[/tex]

Therefore, the percent yield of [tex]P_2O_5[/tex] is, 30.39 %

To determine the percent yield of a reaction, compare the actual yield to the theoretical yield. The theoretical yield can be calculated using stoichiometry and the balanced equation. In this case, the percent yield is 60.7%.

To determine the percent yield of a reaction, you need to compare the actual yield to the theoretical yield. The theoretical yield is the maximum amount of product that can be formed according to the stoichiometry of the balanced equation. In this case, the balanced equation is 4 P + 5 O2 → 2 P2O5. The molar mass of P2O5 is 141.944 g/mol, so the theoretical yield can be calculated as:

Therefore, the theoretical yield is 6.41 g P2O5. To calculate the percent yield, divide the actual yield by the theoretical yield and multiply by 100:

Percent Yield = (Actual Yield ÷ Theoretical Yield) × 100
Percent Yield = (3.89 g ÷ 6.41 g) × 100 = 60.7%

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Answer: Volume of the flask is 31.34 mL.

Explanation:

Weight of empty flask [tex]w_1[/tex]  = 56.12 grams

Weight of flask with water  [tex]w_2[/tex] = 87.39 grams

Weight of water [tex]w_3[/tex] = [tex]w_2-w_1[/tex]  = (87.39 - 56.12) grams= 31.27 grams  

Density of water =  0.9976 g/mL

0.9976 grams are contained in = 1 ml of water

Thus 31.27 grams  are contained in = [tex]\frac{1}{0.9976}\times 31.27=31.34[/tex] ml of water.

Thus the volume of the flask is 31.34 mL.

The volume of the flask is calculated by subtracting the mass of the empty flask from the mass of the filled flask and then dividing by the density of water. The resulting volume is approximately 31.36 mL.

To calculate the volume of the flask in mL, we need to use the mass of the water that filled the flask and the known density of water. First, we find the mass of the water by subtracting the mass of the empty flask from the mass of the filled flask. Then, we use the density formula, which is Density = Mass/Volume, to find the volume of the flask.

Here's the step-by-step calculation:

Determine the mass of the water by subtracting the mass of the empty flask from the filled flask: 87.39 g - 56.12 g = 31.27 g.

Using the known density of water (0.9976 g/mL), calculate the volume using the formula Volume = Mass/Density.

Volume of water (Volume of flask) = 31.27 g / 0.9976 g/mL = 31.36 mL.

Therefore, the volume of the flask is approximately 31.36 mL.

Answer: 12.5

Explanation:

Molarity of a solution is defined as the number of moles of solute dissolved per Liter of the solution.

[tex]Molarity=\frac{moles}{\text {Volume in L}}[/tex]

moles of [tex]NaOH=Molarity\times {\text {Volume in L}}=3.412\times 5.865\times 10^{-3}L=0.02moles[/tex]

moles of [tex]HCl=Molarity\times {\text {Volume in L}}=1.564\times 10^{-3}\times 0.5000L=0.782\times 10^{-3}moles[/tex]

[tex]NaOH+HCl\rightarrow NaCl+H_2O[/tex]

According to stoichiometry:  

1 mole of [tex]HCl[/tex]  require 1 mole of [tex]NaOH[/tex]

Thus [tex]0.782\times 10^{-3}moles[/tex]  will combine with  [tex]0.782\times 10^{-3}moles[/tex]  of [tex]NaOH[/tex]

Thus [tex](0.02-0.782\times 10^{-3})moles=0.019moles[/tex] of [tex]NaOH[/tex] will be left

Thus Molarity of [tex]OH^-=\frac{0.019}{0.56L}=0.03M[/tex]

[tex]pOH=-\log[OH^-][/tex]

Putting in the values:

[tex]pOH=-\log[0.03][/tex]

[tex]pOH=1.5[/tex]

[tex]pH+pOH=14[/tex]

[tex]pH=14-1.5=12.5[/tex]

Thus final pH will be 12.5.

Answer:

1.930 * 10⁻⁹ mg of Mn⁺² are left unprecipitated.

Explanation:

The reaction that takes place is:

Mn⁺² + S⁻² ⇄ MnS(s)  

ksp = [Mn⁺²] [S⁻²]

If the pksp of MnS is 13.500, then the ksp is:

[tex]ksp=10^{-13.500}=3.1623*10^{-14}[/tex]

From the problem we know that [S⁻²] = 0.0900 M

We use the ksp to calculate [Mn⁺²]:

3.1623*10⁻¹⁴= [Mn⁺²] * 0.0900 M

[Mn⁺²] = 3.514 * 10⁻¹³ M.

Now we can calculate the mass of Mn⁺², using the volume, concentration and atomic weight. Thus the mass of Mn⁺² left unprecipitated is:

3.514 * 10⁻¹³ M * 0.1 L * 54.94 g/mol = 1.930 * 10⁻¹² g = 1.930 * 10⁻⁹ mg.

Answer:

The 95% confidence level is

[tex]4.17 \pm 0.2744[/tex]

Explanation:

If we can apply the central limit theorem, we can approximate this distribution to a normal distribution.

The confidence level (for n=1) is defined as

[tex]X\pm \frac{z*\sigma}{\sqrt{n}}=X\pm z*\sigma[/tex]

For a 95% confidence interval, according to the normal distribution, z=1.96.

Then we have:

[tex]X\pm z*\sigma=4.17 \pm 1.96*0.14=4.17 \pm 0.2744[/tex]

Final answer:

To calculate the 95% confidence interval for a set of measurements with a mean of 3.095 g and a standard deviation of 0.0346 g, you first determine the standard error, then use it to find the margin of error, and finally compute the confidence interval, yielding an estimate that the true mean weight of a penny lies between 3.088 and 3.102 g.

Explanation:

To find the 95% confidence interval for a set of measurements, you utilize statistical principles that involve the mean, standard deviation, and sample size of the data. The basic formula to calculate the confidence interval is mean ± (critical value) * (standard deviation / √n), where √n is the square root of the sample size, and the critical value is determined based on the confidence level. For a 95% confidence level, the critical value (often represented as a z-score in the context of a normal distribution) is approximately 1.96.

Let's assume you're working with a sample size large enough for the central limit theorem to apply, simplifying the computation of the confidence interval to just involving the mean and standard deviation, due to a large sample size making the distribution of sample means approximately normal. Therefore, for the sample of 100 pennies with a mean of 3.095 g and a standard deviation of 0.0346 g, the 95% confidence interval can be calculated as follows:

This calculation reveals that we estimate with 95% confidence that the true mean weight of a penny lies between 3.088 and 3.102 g.

Answer:

1,816 L

Explanation:

Molar concentration or molarity is a way to express the concentration of a chemical in terms of moles of substances per liter of solution.

To obtain the liters of this solution you must convert moles/L to g/L with formula weight (FW), thus:

0,1107 mol of KCl / L × (74,6 g / mol) = 8,258 g of KCl / L.

It means that in one liter you have 8,258 g of KCl. Thus, 15,00 g of KCl are contained in:

15,00 g × (1 L / 8,258 g) = 1,816 L

I hope it helps!

Explanation:

The given data is as follows.

               MW = 29 g/mol,         [tex]C_{p}[/tex] = 3.5 R

Formula to calculate minimum amount of work is as follows.

            [tex]W_{s} = C_{p}T_{1}[(\frac{P_{2}}{P_{1}})^{\frac{R}{C_{p}}} - 1][/tex]

                          = [tex]3.5 \times 8.314 J/k mol \times 306 \times [(\frac{550}{125})^{\frac{1}{3.5}} - 1][/tex]

                          = 4.692 kJ/mol

Therefore, total work done will be calculated as follows.

                        Total work done = [tex]m \times W_{s}[/tex]

Since, m = [tex]\frac{150 \times 10^{3}g/min}{29}[/tex]. Therefore, putting these values into the above formula as follows.

            Total work done = [tex]m \times W_{s}[/tex]

                                        = [tex]\frac{150 \times 10^{3}g/min}{29} \times 4.692 kJ/min[/tex]      

                                       = 24268.96 kJ/min

It is known that 1 kJ/min = 0.0166 kW. Hence, convert 24268.96 kJ/min into kW as follows.

                   [tex]24268.96 kJ/min \times \frac{0.0166 kW}{1 kJ/min}[/tex]                                                    

                   = 402.86 kW

Thus, we can conclude that the minimum work required by an air compressor is 402.86 kW.

Answer:

a)Number average molecular weight is 50, 500 g/mol

b) Weight average molecular weight is 99, 019.8 g/mol

Explanation:

We have a polymer P made up of two monodisperse fractions.

A with molecular weight of MA = 1000 g/mol and B with MB =100000 g/mol.  

The batch contains an equal mole fraction of each component A and B.  

Let's suppose a total number (Nt) of mols 2 moles. Equal fraction means XA = 0.5 and XB =0.5

Nt = 2 mol

Na = 2*0.5 = 1 mol

Nb = 2*0.5 = 1 mol.

So, we have 1 mol of A, 1 mol of B and 2 moles in total.  

a) The number average molecular weight (NAM) is calculate using the mole numbers of each component. In this case, we will multiple each component molecular weight by the number of moles of each one. After that we will sum them and finally to divide by the total number of moles.

NAM = (Na*MA + Nb*MB)/(Nt)

NAM = (1 mol *1000 g/mol + 1*100000 g/mol ) /(2 mol)

NAM = 50500 g/mol

The number average molecular weight for the polymer P is 50,500 g/mol

b) Weight average molecular weight (WAM) is calculated using the mass quantities of each component. Weight mass of A (WA), weight mass of B (WB) are calculate using the moles of A, B and their molecular weights respectively. Total Weight (WT)

WA = Na*MA = 1 mol *1000 g/mol = 1000 g A

WB = Nb*MB = 1mol * 100000 g/mol = 100 000 gB

WT = WA + WB = 101 000 g

Now we will calculate average molecular using weights, we will multiple each component molecular weight by the mass of each one. After that we will sum them and finally to divide by the total mass.

WAM = (WA*MA + WB*MB)/(WT)

WAM = (1000 g *1000 g/mol + 100000 g*100000 g/mol )/(101 000 g)

WAM = 99 019.8 g/mol

The weight average molecular weight for polymer P is 99, 019.8 g/mol

Final answer:

The number average molecular weight (Mn) for the polymer is 50,500 g/mol, while the weight average molecular weight (Mw) is 198,019,802 g/mol, given the equal mole fraction of the two monomer fractions.

Explanation:

The  number average molecular weight (Mn) and the weight average molecular weight (Mw) of a polymer comprising two monodisperse fractions.

Firstly, to calculate the Mn, we consider the definition that Mn is the total weight of the polymer divided by the total number of moles. Since each fraction has an equal mole fraction, we take the simple average of the two given molecular weights:

Next, to compute the Mw, which is the sum of the products of the weight contribution of each fraction and its molecular weight squared, divided by the total weight:

To summarize, for a polymer with an equal mole fraction of two fractions with molecular weights of 1000 g/mol and 100,000 g/mol, the number average molecular weight is 50,500 g/mol and the weight average molecular weight is 198,019,802 g/mol.

Answer: 72.41% and 26.90% respectively.

Explanation:

At 60°C, you can dissolve 46.4g of acetanilide in 100mL of ethanol. If you lower the temperature, at 0°C, you can dissolve just 12.8g, which means (46.4g-12.8g)=33.6g of acetanilide must have precipitated from the solution.

We can calculate recovery as:

[tex]\%R=\frac{crystalized\ mass}{initial\ mass}*100 =\frac{33.6\ g}{46.4\ g}*100=72.41\%[/tex]

So the answer to the first question is 72.41%.

For the second part just use the same formula, the mass of the precipitate is the final mass minus the initial mass, (171mg-125mg)=46mg.

[tex]\%R=\frac{crystalized\ mass}{initial\ mass}*100 =\frac{46\ mg}{171\ mg}*100=26.90\%[/tex]

So the answer to the second question is 26.90%.

Explanation:

According to the ideal gas equation, PV = nRT.

where,     P = pressure,        V = volume

               n = no. of moles,      R = gas constant

               T = temperature

Also, density is equal to mass divided by volume. And, no. of moles equals mass divided by molar mass.

Therefore, then formula for ideal gas could also be as follows.

                 P = [tex]\frac{mass}{volume \times molar mass} \times RT[/tex]

or,             P = [tex]\frac{density}{\text{molar mass}} \times RT[/tex]

Since, density is given as 0.789 g/ml which is also equal to 789 g/L (as 1000 mL = 1 L). Hence, putting the given values into the above formula as follows.

               P = [tex]\frac{density}{\text{molar mass}} \times RT[/tex]

                  = [tex]\frac{789 g/l}{46.06 g/mol} \times 0.0821 L atm/mol K \times 373 K[/tex]

                  = 525 atm

As two-liter soft drink bottle can withstand a pressure of  5 atm and the value of calculated pressure is 525 atm which is much greater than 5 atm.

Therefore, the soft drink bottle will  obviously explode.

Explanation:

The electronic configuration of sodium with Z = 11 is : 2, 8, 1

The electronic configuration of chlorine with Z = 17 is : 2, 8, 7

The Lewis structure is drawn in such a way that the octet of each atom is complete.

Thus, sodium losses one electron to chlorine and chlorine accepts this electron to form ionic bond.

Thus, the valence electrons are shown by dots in Lewis structure. The structure is shown in image below.

The Lewis structure of NaCl involves sodium losing one electron to become Na+ and chlorine gaining one electron to become Cl-. Draw the ions next to each other to represent the ionic bond. Sodium has no electrons around it while chlorine has a complete octet with the extra electron in brackets.

The Lewis structure of sodium chloride (NaCl), follow these steps:

Na: Na+ [ ]

Cl: [ :Cl: ]-

Note that the brackets around the chlorine indicate it has gained an electron and the overall charge of the ion.

Answer:

None of the above

Explanation:

Henry's law -

This law was given by William Henry in the year 1803 , it is also known as the gas law ,

According to Henry's law , the amount of gas which gets dissolved in a liquid is directly related to the partial pressure of gas that is in equilibrium with the liquid , at a constant temperature .

Or it can stated as ,

The gases' solubility in a liquid is directly related to the partial pressure of gas that is in equilibrium with the liquid .

This law is applicable for sparingly soluble gases in liquid solvents .

And the solubility of a gas is independent of temperature and pressure .

Hence ,

the correct option is None of the above .

Explanation:

It is given that flow rate is 10,000 L/s. As 1 L equals 0.001 [tex]m^{3}[/tex].

Hence, flow rate will be 10 [tex]m^{3}/s[/tex]. Calculate mass of water flowing per second as follows.

        Mass flowing per second = density × flow rate

                                                   = [tex]1000 kg/m^{3} \times 10 m^{3}/s[/tex]

                                                   = [tex]10^{4} kg/s[/tex]

Also, energy provided per second will be as follows.

                      E = mgh

Putting the given values into the above formula as follows.

                   E = mgh

                      = [tex]10^{4} kg/s \times 9.8 m/s^{2} \times 75 m[/tex]  

                       = [tex]735 \times 10^{4} W[/tex]

or,                    = 7350 kW

Thus, we can conclude that energy per unit time provided will be 7350 kW.                

Answer:

density = 7.55 g/cm^3

Explanation:

we need to get the volume first to get the density , and the volume formula is:

the volume = area * thickness

where :

area = 2 cm * 2 cm = 4 cm^2

and thickness = 100 cm

by substitution:

the volume = 4 * 100 = 400 cm^3

where

density = mass / volume

we have to convert mass from kg to g = 3020 g

by substitution:

density = 3020 g / 400 cm^3

           = 7.55 g/cm^3

Answer:

0.712 moles of NO₂ are formed.

Explanation:

First, we need to write the balanced equation:

2 N₂O₅(g) ⇄ 4 NO₂(g) + O₂(g)

From the balanced equation, we can see the relationship between the moles of N₂O₅ and the moles of NO₂. Every 2 moles of N₂O₅ that react, 4 moles of NO₂ are formed. Let us apply this relationship to the information given by the problem (0.356 moles of N₂O₅):

[tex]0.356molN_{2}O_{5}.\frac{4molNO_{2}}{2molN_{2}O_{5}} =0.712molNO_{2}[/tex]

Answer:

2.6 sec

Explanation:

The distance between the Earth and the moon = 240,000 miles

Also,

1 mile = 1609.34 m

So,

Distance between the Earth and the moon = 240,000 ×  1609.34 m = 386241600 m

Speed of the light = 3 × 10⁸ m/s

Distance = Speed × Time.

So,

Time = Distance / Speed = 386241600 m / 3 × 10⁸ m/s = 1.3 sec

For back journey = 1.3 sec

So, total time = 2.6 sec

Answer:

Tube 2 has a total dilution of 1:50

Explanation:

We have a 2 ml serum sample added to a 18 mL phosphate buffered saline sample in tube 1. This means now in tube 1 there is 20 mL.

We have a 1:10 (= 2:20) dilution here.

10 ml of this 1:10 diluted tube 1 is taken and added to a 40 mL of PBS in tube 2.

Now we have 50 mL in tube 2.

This is a 10:50 (= 1:5) dilution.

The total dilution is 10x5 = 50

So the total ditultion has a rate 1:50

Tube 2 has a total dilution of 1:50

Answer:

All of them can be necessary.

Explanation:

In typical DNA cloning, the gene of interest is inserted into a plasmid, this is achieved by using enzymes that "cut and paste" DNA producing a recombinant DNA, considering this we will first need a DNA fragment to be cloned. To "cut and paste" these fragments of DNA we will need restriction enzymes (to cut) and DNA ligase (to paste), this enzyme will recognize the specific target sequence and I'll cut it, another restriction enzyme will also cut the plasmid, then DNA ligase will link the plasmid and target gene together. Now we need to introduce the plasmid into bacteria, to extract it we use glucose as a buffer to maintain the pH-controlled for the plasmid to be stable, so that linear dsDNA (sheared chromosomal DNA) is denatured but closed-circular DNA (plasmid) is not. Once we have our plasmid isolated we can put it into our bacteria (this is called transformation), this is achieved by giving the bacteria a shock that encourages them to take foreign DNA, calcium chloride can improve the results by binding plasmids to lipopolysaccharides in the bacteria. After this shock, some bacteria will accept the plasmid but a portion won't, this is why plasmids typically contain antibiotic resistance genes to allow the bacteria that contain the plasmids to survive after the application of such antibiotic, this means ampicillin is also necessary to isolate our bacteria with recombinant DNA. Finally, you can use these bacteria as "factories" to produce proteins and then obtain them by splitting the bacteria, to achieve this splitting we can use proteases, for example, chymotrypsin. NOw you'll need to purify the proteins you extract one method to do it is using the starch binding domain (SBD) that can be found in some amylolytic enzymes, we can add a recombinant proteins for transferring the starch binding capacity to the target proteins, we will observe both proteins fused to the SBDtag, only the target protein will remain over the starch granules after the wash process.

I hope you find this information useful and interesting! good luck!