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.
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]
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
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
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.
The solubility product constant of pbcl2 is 1.7 × 10−5 . what is the maximum concentration of pb2+ that can be in ocean water that contains 0.0500 m nacl?
Define atom. list the subatomic particles, describe their relative masses,charges, and positions in the atom.
What is the molarity of 555 l of a ba(oh)2 solution if the ph is 10.20? 1. 2.26 × 10−5 m 2. 6.31 × 10−11 m 3. 5.15 × 10−7 m 4. 3.15 × 10−11 m 5. 3.14 × 10−4 m 6. 1.58 × 10−4 m 7. 7.92 × 10−5 m 8. 4.40 × 10−2 m?
Answer:
7. 7.92 × 10−5
Explanation:
Hello,
In this case, with the given pH, one could find the pOH:
[tex]pOH=14-pH=14-10.20=3.8[/tex]
Thus, since barium hydroxide is completely dissolved in water based on:
[tex]Ba(OH)_2\rightarrow Ba^{+2}+2OH^-[/tex]
The concentration of hydroxyl ions is twice to that of the hydroxide (2:1 mole relationship). Therefore, by considering the relationship between the pOH and the concentration of hydroxyl we have:
[tex]pOH=-log([OH]^-)\\[/tex]
[tex][OH]^-=10^{-3.8}=1.58x10^{-4}M[/tex]
Finally, given the 1:2 mole ratio of barium hydroxide to hydroxyl ions, the concentration of barium hydroxide results:
[tex][Ba(OH)_2]=2*[OH^-]=\frac{1}{2} *1.58x10^{-4}M[/tex]
[tex][Ba(OH)_2]=7.92x10^{-5}M[/tex]
Thus, the answer is 7. 7.92 × 10−5.
Regards.
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?
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
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.
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/molPlugging 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.
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.
The first one is chlorine ion, the second one is metal ion.
In a laboratory experiment, John uses a mesh to separate soil particles from water. Which technique of separation is he using? chromatography distillation filtration fragmentation condensation
Answer: Option (c) is the correct answer.
Explanation:
A mesh is a kind of net like structure generally used for the purpose of filtration.
Distillation is defined as the method used to separate two liquids with a difference of less than or around [tex]25^{o}C[/tex] in their boiling point.
So, a liquid with low boiling point will evaporate and its vapors can be collected in a separate container.
Chromatography is defined as a method for separating a mixture by passing it in a solution with the help of a medium where the components of the mixture travel at different rates.
And, filtration is a method used to separate a solid from a liquid by passing through a porous barrier. The solid remain stick to the barrier and liquid passes through the barrier.
A method in which a solid substance is broken down into different parts or fragments is known as fragmentation.
Condensation is a process is in which vapor phase of a substance changes into liquid phase.
Thus, we can conclude that in the given situation John is using the technique of filtration.
which of the following is a balanced chemical equation for the reaction of magnesium with nitrogen gas to form magnesium nitride
The reaction of cr2+(aq) with cr2o2−7(aq) in acid solution to form cr3+(aq). calculate δg∘rxn.
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 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?
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.
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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
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.
what is the volume of 12.0 g of cl2 gas at stp
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.
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
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
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.
Carl crumbled a piece of paper before throwing it in the trash can. Which is true about the paper after it has been crumbled
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.
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
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
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.
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.
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if you have 100 grams of S8, how many moles of S8 is that
How many carbon-carbon sigma bonds are present in each of the following molecules: benzene, cyclobutane?
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.
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.
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?
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.
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]
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
In the lewis structure of ch3oh, how many bonding pairs of electrons are there?
the number of atoms bonded to the central atom is 4
Explanation:
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.
Mercury is a pollutant classified as
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
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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Determine if the bond between each pairs of atoms would be pure covalent, polar covalent, or ionic. n and se
Types of Bonds can be predicted by calculating the difference in electronegativity.
If, Electronegativity difference is,
Less than 0.4 then it is Non Polar Covalent Bond
Between 0.4 and 1.7 then it is Polar Covalent Bond
Greater than 1.7 then it is Ionic
For N and Se,
E.N of Nitrogen = 3.04
E.N of Selenium = 2.55
________
E.N Difference 0.49 (Weakly Polar Covalent)
As you have not provided remaining pairs, so if you have any of them, follow the method as mentioned above.
Pure covalent bond is formed between Br and Br. Polar covalent bonds are formed by O and F, N and Cl, and others. A connection between Sr and O is ionic.
We can take into account the difference in electronegativity between the elements involved to determine the sort of bond—pure covalent, polar covalent, or ionic—between each pair of atoms:
The terms "Br and Br" (bromine and bromine)
Since both atoms are composed of the same element, their electronegativity is the same.
The difference in electronegativity is 0.
Because the identical atoms share the electrons evenly, a pure covalent link is produced.
Oxygen and fluorine, or O and F:
The electronegativity of oxygen (O) is roughly 3.44.
With a value of roughly 3.98, fluorine (F) has a higher electronegativity.
O and F have different electronegativities by 0.54.
This slight difference in electronegativity points to a polar covalent connection, where the electrons are distributed unevenly, leaving the less electronegative atom (O) with a partial positive charge and the more electronegative atom (F) with a partial negative charge.
Nitrogen and chlorine, or N and Cl
The electronegativity of nitrogen (N) is around 3.04.
The electronegativity of chlorine (Cl) is roughly 3.16.
N and Cl have different electronegativities of 0.12 each.
This slight variation in electronegativity suggests a polar covalent connection, similar to that between O and F.
Oxygen and strontium are two elements.
About 0.95 is the electronegativity of strontium (Sr).
With a value of about 3.44, oxygen (O) has a much higher electronegativity.
Between Sr and O, there is a significant difference in electronegativity (3.44 - 0.95 = 2.49).
The creation of Sr²⁺ ions and O₂ ions, which are bound together by electrostatic forces, results from the electrons being transferred from Sr to O in an ionic bond, as indicated by the high electronegativity difference.
To sum up:
Pure covalent bond is formed between Br and Br.
Polar covalent bonds are formed by O and F, N and Cl, and others.
A connection between Sr and O is ionic.
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