Problem 30 - Chemistry: Principles and Reactions

Question

The equation for the iodination of acetone in acidic solution is $$\mathrm{CH}_{3} \mathrm{COCH}_{3}(a q)+\mathrm{I}_{2}(a q) \longrightarrow \mathrm{CH}_{3} \mathrm{COCH}_{2} \mathrm{I}(a q)+\mathrm{H}^{+}(a q)+\mathrm{I}^{-}(a q)$$ The rate of the reaction is found to be dependent not only on the concentration of the reactants but also on the hydrogen ion concentration. Hence the rate expression of this reaction is $$\text { rate }=k\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]^{m}\left[\mathrm{I}_{2}\right]^{n}\left[\mathrm{H}^{+}\right]^{p}$$ The rate is obtained by following the disappearance of iodine using starch as an indicator. The following data are obtained: $$ \begin{array}{cccc} \hline\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right] & \left.\mathrm{[H}^{+}\right] & {\left[\mathrm{I}_{2}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\ \hline 0.80 & 0.20 & 0.001 & 4.2 \times 10^{-6} \\ 1.6 & 0.20 & 0.001 & 8.2 \times 10^{-6} \\ 0.80 & 0.40 & 0.001 & 8.7 \times 10^{-6} \\ 0.80 & 0.20 & 0.0005 & 4.3 \times 10^{-6} \\ \hline\end{array}$$ (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 rate of the reaction when \(\left[\mathrm{H}^{+}\right]=0.933 M\) and \(\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]=3\left[\mathrm{H}^{+}\right]=10\left[\mathrm{I}^{-}\right] ?\)

Step-by-Step Solution

Answer

Answer: The orders of the reaction are as follows: with respect to CH3COCH3, the order is 1, with respect to H+, the order is 1, and with respect to I2, the order is 2.

Step 1: (a) Determine the order of the reaction with respect to each reactant

To determine the order of the reaction with respect to each reactant, we need to examine how the initial rate changes when the concentration of a single reactant is changed. Let's compare experiments 1 & 2 and experiments 1 & 3. For CH3COCH3: Experiments 1 & 2: $$\frac{(\text{Rate 2})}{(\text{Rate 1})} = \frac{8.2 \times 10^{-6}}{4.2 \times 10^{-6}} = 1.952$$ $$\frac{\left[\mathrm{CH}_{3}\mathrm{COCH}_{3}\right]_{2}}{\left[\mathrm{CH}_{3}\mathrm{COCH}_{3}\right]_{1}} = \frac{1.6}{0.8} = 2$$ Since the ratio of the rates is approximately equal to the ratio of the concentrations, the order \(m\) of the reaction with respect to CH3COCH3 is 1. For H+: Experiments 1 & 3: $$\frac{(\text{Rate 3})}{(\text{Rate 1})} = \frac{8.7 \times 10^{-6}}{4.2 \times 10^{-6}} = 2.071$$ $$\frac{\left[H^{+}\right]_{3}}{\left[H^{+}\right]_{1}} = \frac{0.4}{0.2} = 2$$ Since the ratio of the rates is approximately equal to the ratio of the concentrations, the order \(p\) of the reaction with respect to H+ is 1. For I2: Experiments 1 & 4: $$\frac{(\text{Rate 4})}{(\text{Rate 1})} = \frac{4.3 \times 10^{-6}}{4.2 \times 10^{-6}} = 1.024$$ $$\frac{\left[I_2\right]_{4}}{\left[I_2\right]_{1}} = \frac{0.0005}{0.001} = 0.5$$ Since the ratio of the rates is approximately equal to the square root of the ratio of the concentrations, the order \(n\) of the reaction with respect to I2 is 2.

Step 2: (b) Write the rate expression for the reaction

Now that we have determined the order of the reaction with respect to each reactant, we can write the rate expression: $$\text{rate} = k\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]^{1}\left[\mathrm{I}_{2}\right]^{2}\left[\mathrm{H}^{+}\right]^{1}$$

Step 3: (c) Calculate \(k\)

We will use the data from experiment 1 to calculate the rate constant k. $$\text{rate} = k\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{I}_{2}\right]^{2}\left[\mathrm{H}^{+}\right]$$ $$k = \frac{\text{rate}}{\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{I}_{2}\right]^{2}\left[\mathrm{H}^{+}\right]} = \frac{4.2 \times 10^{-6}}{(0.80)(0.001)^{2}(0.20)} = 2.625 \times 10^{-2} M^{-2}s^{-1}$$ So, the rate constant \(k = 2.625 \times 10^{-2} M^{-2}s^{-1}\).

Step 4: (d) What is the rate of the reaction under given conditions?

To find the rate of the reaction under given conditions, we must use the rate expression obtained in step (b) and the provided concentrations: \(\left[H^{+}\right]=0.933 M\), \(\left[\mathrm{CH}_{3}\mathrm{COCH}_{3}\right]=3\left[H^{+}\right]=2.799 M\), and \(\left[I^{-}\right]=0.1\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right] = 0.2799 M\). Since I− is a product, its concentration won't affect the rate. The rate expression can be written as: $$\text{rate} = k\left[\mathrm{CH}_{3} \mathrm{COCH}_{3}\right]\left[\mathrm{I}_{2}\right]^{2}\left[\mathrm{H}^{+}\right]$$ $$\text{rate} = (2.625 \times 10^{-2} M^{-2}s^{-1})(2.799 M)(0.2799 M)^{2}(0.933 M) = 1.98 \times 10^{-2} M.s^{-1}$$ So, the rate of the reaction under given conditions is \(1.98 \times 10^{-2} M.s^{-1}\).

Key Concepts

Reaction Rate

The rate of a reaction indicates how quickly reactants turn into products. In this context, it measures the disappearance of iodine in the iodination of acetone. Knowing the reaction rate helps us understand how fast or slow a chemical process occurs.
A few factors influence reaction rate:

• Concentration: The higher the concentration of reactants, the higher the number of collisions between them, often increasing the reaction rate.
• Temperature: Generally, increasing temperature speeds up reactions because particles move faster and collide more frequently.
• Catalysts: These substances can speed up reactions without being consumed.

In this exercise, the reaction rate is related to concentrations of acetone \([\mathrm{CH}_{3} \mathrm{COCH}_{3}]\), iodine \([\mathrm{I}_{2}]\), and hydrogen ions \([\mathrm{H}^{+}]\). Understanding reaction rate helps predict the progress of chemical reactions in various conditions.

Order of Reaction

The order of reaction reflects how the rate is affected by the concentration of reactants.
It is determined experimentally by observing changes in the reaction rate as the concentration of one reactant is varied while others are held constant.
Here's how it works:

• If a reaction is first order with respect to a reactant, the rate is directly proportional to its concentration.
• A second order reaction means the rate is proportional to the square of the concentration.
• Zeroth order reactions mean that concentration changes do not affect the rate.

In the iodination of acetone, experiments showed that:
1. The reaction is first order with respect to acetone and hydrogen ions.
2. It is second order concerning iodine.
This means that doubling the concentration of acetone or hydrogen ions doubles the rate. Doubling the concentration of iodine increases the rate by a factor of four due to its second-order behavior.

Rate Constant

The rate constant, denoted as \(k\), is a crucial part of the rate equation. It ties the order of reaction to the actual rates.
A key point is that the rate constant has different units depending on the overall order of the reaction. For this exercise, the rate constant was calculated using:
\[ k = \frac{\text{rate}}{[\text{Acetone}][\text{Iodine}]^{2}[\text{H}^{+}]} \]
For a reaction with orders \(m\), \(n\), and \(p\) in different reactants, the units of \(k\) ensure that the rate (\