The equation for the reaction between iodide and bromate...

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 $\left[\mathrm{I}^{-}\right]=\left[\mathrm{BrO}_{3}^{-}\right]=0.0075 \mathrm{M} ?$

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 $\left[\mathrm{I}^{-}\right]=\left[\mathrm{BrO}_{3}^{-}\right]=0.0075 \mathrm{M} ?$

Key Concepts

Reaction Order

The reaction order defines how the rate of a chemical reaction depends on the concentration of each reactant. It is determined experimentally by measuring the change in the reaction rate as the concentration of one reactant is varied while keeping others constant. The orders with respect to each reactant indicate the power to which its concentration is raised in the rate law, and the sum of these gives the overall order of the reaction.

Rate Law Expression

The rate law expression mathematically relates the rate of a reaction to the concentrations of its reactants. It typically takes the form Rate = k [A]^m [B]^n [C]^p, where m, n, and p are the reaction orders with respect to reactants A, B, and C, respectively, and k is the rate constant. Determining the rate law requires experimental data because it cannot always be deduced from the balanced chemical equation.

Rate Constant (k) Calculation

The rate constant, k, is a proportionality factor in the rate law that is unique to a given reaction at a specified temperature. To calculate k, experimental data for initial rates and reactant concentrations are substituted into the rate law equation. The value of k, along with its units, depends on the overall order of the reaction and reflects factors such as temperature and activation energy.

Units and Dimensional Analysis

The units of the rate constant k depend on the overall order of the reaction. For example, in a reaction of order n, the units of k are typically expressed as L^(n-1) mol^(1-n) s^(-1). Dimensional analysis is used to ensure consistency throughout the rate law expression and to correctly interpret the kinetic parameters obtained from experimental data.

Transcript

00:01 All right, so here we are given the data from the reaction rate measuring of the disappearance of hydrogen gas.

00:14 We're measuring the appearance and we have the reaction rate values.

00:18 Now, in general, the rate law is given as r equals k, the concentration of the reactant, that's i minus raised to the power of x times bro3 minus raised to the power of y.

00:37 And of course, hydrogen ions raised to the power of z, where x, y, and z are orders of the reaction with respect to each of those reactants.

00:48 Now, for us to be able to determine this, we're gonna have to pick each of the data that we're given, right? one after the other, you know, just and apply it.

01:01 So we're gonna use each experiment to determine which data will be appropriate.

01:07 For example, to determine the order of the reaction with respect to iodide ion, we would need to pick the first data and the second because you see that the concentrations of the other reactants are kept constant.

01:23 So for example, so that means for r1, we would have the rate of the reaction.

01:27 There was 8 .89 times 10 to the power of minus five.

01:33 And this would be k times the concentration of a myodide ion there was 0 .0020 raised to the power of x.

01:43 We don't know what that is, right? and the second data, we're dividing that.

01:49 That was 1 .78, 1 .78 times 10 to the power of minus four.

01:57 And the rate concentration was 0 .004 raised to the power x.

02:05 Now, when you divide this, you would have this to be 0 .499 or 0 .5.

02:10 And this would be 0 .05 raised to the power x, right? k and this will cancel out.

02:17 Now, if you take a look at both sides, you'll find that that x would be log of basically 0 .5 divided by 0 .05.

02:27 And this will give you about 0 .23, which is we can say approximately zero, right? approximately zero, approximately.

02:35 Good, so if that's the case, it means that the order of the reaction with respect to the iodide ion is zero, which means the changes in concentration of the iodide ion does not affect the rate of the reaction.

02:49 That's what it means.

02:51 Okay, so let's try the next one.

02:53 For the bromate ion, the bro3 minus, we're going to need the first and the third, right? so it means that we'll be looking at 8 .89 times 10 to the power of minus five and equals to k, the concentration of the bromate ion at that point was 0 .008 raised to the power of y.

03:22 But third data, we have 1 .78, 1 .78 times 10 to the power of minus four.

03:30 And that was k, we're dividing that 0 .016 raised to the power of y.

03:37 Again, this would give you 0 .5 approximately.

03:41 And this would give you, of course, k will cancel, but of course you have 0 .5 also, right? this is also 0 .5 raised to the power of y.

03:54 So you see that this is raised to the power of one, so meaning that y is one.

03:59 So this is first order.

04:01 This is for the bromate ion, right? this is for the bromate ion...