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Chapter 11: Problem 6

For the reaction \(5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_{2}(a q)+3 \mathrm{H}_{2} \mathrm{O}\) It was found that at a particular instant, bromine was being formed at the rate of \(0.029 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\). At that instant, at what rate (a) are the hydrogen ions being consumed? (b) is water being formed? (c) are the bromide ions being consumed?

Short Answer

Expert verified
Answer: At the given instant, the rate of Hydrogen ion consumption is 0.058 mol/L*s, the rate of Water formation is 0.029 mol/L*s, and the rate of Bromide ion consumption is 0.0483 mol/L*s.

Step by step solution

01

(Step 1: Write the given balanced chemical equation)

The balanced chemical equation is as follows: \(5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_{2}(a q)+3 \mathrm{H}_{2} \mathrm{O}\)
02

(Step 2: Determine the rate of Bromine formation)

It is given that Bromine is being formed at the rate of \(0.029 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\). It can be represented as, Rate of \(\mathrm{Br}_2\) formation = \(0.029 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\)
03

(Step 3: Calculate the rate of Hydrogen ions consumption)

From the balanced chemical equation, we can see that 6 moles of Hydrogen ions are consumed for every 3 moles of Bromine formed. Therefore, we can set up the ratio as follows: Rate of \(\mathrm{H}^{+}\) consumption : Rate of \(\mathrm{Br}_2\) formation = 6 : 3 Now, we can find the rate of \(\mathrm{H}^{+}\) consumption by multiplying the rate of \(\mathrm{Br}_2\) formation by the ratio of \(\mathrm{H}^{+}\) consumption to \(\mathrm{Br}_2\) formation: Rate of \(\mathrm{H}^{+}\) consumption = \(0.029 \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}} \cdot \frac{6}{3} = 0.058 \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}}\)
04

(Step 4: Calculate the rate of Water formation)

From the balanced chemical equation, we see that 3 moles of Water are formed for every 3 moles of Bromine formed. Thus, the ratio is as follows: Rate of Water formation : Rate of \(\mathrm{Br}_2\) formation = 3 : 3 Rate of Water formation = \(0.029 \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}} \cdot \frac{3}{3} = 0.029 \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}}\)
05

(Step 5: Calculate the rate of Bromide ion consumption)

From the balanced chemical equation, we can infer that 5 moles of Bromide ions are consumed for every 3 moles of Bromine formed. So, the ratio is as follows: Rate of Bromide ion consumption : Rate of \(\mathrm{Br}_2\) formation = 5 : 3 Rate of Bromide ion consumption = \(0.029 \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}} \cdot \frac{5}{3} = 0.0483\bar{3} \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}}\) Thus, at the given instant: a) The rate at which Hydrogen ions are being consumed is \(0.058 \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}}\). b) The rate at which Water is being formed is \(0.029 \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}}\). c) The rate at which Bromide ions are being consumed is \(0.0483\bar{3} \frac{\mathrm{mol}}{\mathrm{L} \cdot \mathrm{s}}\).

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Most popular questions from this chapter

For the first-order thermal decomposition of ozone $$ \mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g) $$ \(k=3 \times 10^{-26} \mathrm{~s}^{-1}\) at \(25^{\circ} \mathrm{C}\). What is the half-life for this reaction in years? Comment on the likelihood that this reaction contributes to the depletion of the ozone layer.

The equation for the reaction between iodide and bromate ions in acidic solution is \(6 \mathrm{I}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{I}_{2}(a q)+\mathrm{Br}^{-}(a q)+3 \mathrm{H}_{2} \mathrm{O}\) The rate of the reaction is followed by measuring the appearance of \(\mathrm{I}_{2}\). The following data are obtained: $$ \begin{array}{clcc} \hline\left[I^{-}\right] & {\left[\mathrm{BrO}_{3}^{-}\right]} & {\left[\mathrm{H}^{+}\right]} & \text {Initial } \operatorname{Rate}(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\ \hline 0.0020 & 0.0080 & 0.020 & 8.89 \times 10^{-5} \\ 0.0040 & 0.0080 & 0.020 & 1.78 \times 10^{-4} \\ 0.0020 & 0.0160 & 0.020 & 1.78 \times 10^{-4} \\ 0.0020 & 0.0080 & 0.040 & 3.56 \times 10^{-4} \\ 0.0015 & 0.0040 & 0.030 & 7.51 \times 10^{-5} \\ \hline \end{array} $$ (a) What is the order of the reaction with respect to each reactant? (b) Write the rate expression for the reaction. (c) Calculate \(k\). (d) What is the hydrogen ion concentration when the rate is \(5.00 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}\) and \(\left[\mathrm{I}^{-}\right]=\left[\mathrm{BrO}_{3}^{-}\right]=0.0075 \mathrm{M} ?\)

Consider the reaction between nitrogen oxide and oxygen. $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) $$ The rate of the reaction is followed by measuring the appearance of \(\mathrm{NO}_{2}\). The following data are obtained: $$ \begin{array}{cccc} \hline \text { Expt. } & \text { [NO] } & {\left[\mathrm{O}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \text { min }) \\ \hline 1 & 0.0244 & 0.0372 & 2.20 \times 10^{-3} \\ 2 & 0.0244 & 0.0122 & 7.23 \times 10^{-4} \\ 3 & 0.0244 & 0.0262 & 1.55 \times 10^{-3} \\ 4 & 0.0732 & 0.0372 & 1.98 \times 10^{-2} \\ \hline \end{array} $$ (a) What is the order of the reaction with respect to each reactant? (b) Write the rate expression for the reaction. (c) Calculate \(k\) for the reaction. What are the units for \(k\) ? (d) What is the rate of the reaction at the temperature of the experiment when \([\mathrm{NO}]=0.0100 \mathrm{M}\) and \(\left[\mathrm{O}_{2}\right]=0.0462 \mathrm{M} ?\)

The decomposition of sulfuryl chloride, \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\), to sulfur dioxide and chlorine gases is a first-order reaction. $$ \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) $$ At a certain temperature, the half-life of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is \(7.5 \times 10^{2}\) min. Consider a sealed flask with \(122.0 \mathrm{~g}\) of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\). (a) How long will it take to reduce the amount of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) in the sealed flask to \(45.0 \mathrm{~g}\) ? (b) If the decomposition is stopped after \(29.0 \mathrm{~h}\), what volume of \(\mathrm{Cl}_{2}\) at \(27^{\circ} \mathrm{C}\) and 1.00 atm is produced?

Nitrosyl chloride (NOCl) decomposes to nitrogen oxide and chlorine gases. (a) Write a balanced equation using smallest wholenumber coefficients for the decomposition. (b) Write an expression for the reaction rate in terms of \(\Delta[\mathrm{NOCl}]\) (c) The concentration of NOCl drops from \(0.580 \mathrm{M}\) to \(0.238 \mathrm{M}\) in \(8.00 \mathrm{~min} .\) Calculate the average rate of reaction over this time interval.
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