Problem 65 - Chemistry The Science in Context

Question

The reaction between propionaldehyde (CH \(_{3} \mathrm{CH}_{2} \mathrm{CHO}\) ) and hydrocyanic acid (HCN) has been studied in aqueous solution at \(25^{\circ} \mathrm{C}\). Concentrations of reactants as a function of time are shown in the following table. a. What is the average rate of consumption of HCN from \(11.12 \mathrm{min}\) to \(40.35 \mathrm{min} ?\) b. What is the average rate of consumption of propionaldehyde over that same period? $$\begin{array}{ccc} \text { Time (min) } & {\left[\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}\right](\mathrm{M})} & {[\mathrm{HCN}](\mathrm{M})} \\ 3.28 & 0.0384 & 0.0657 \\ \hline 11.12 & 0.0346 & 0.0619 \\ \hline 24.43 & 0.0296 & 0.0569 \\ \hline 40.35 & 0.0242 & 0.0515 \\ \hline 67.22 & 0.0190 & 0.0463 \\ \hline \end{array}$$

Step-by-Step Solution

Answer

Answer: The average rate of consumption of HCN between 11.12 minutes and 40.35 minutes is 3.56 x 10^{-4} M/min, and the average rate of consumption of propionaldehyde during the same period is also 3.56 x 10^{-4} M/min.

Step 1: Identifying the needed concentration values.

The concentrations of propionaldehyde and hydrocyanic acid (HCN) at 11.12 minutes and 40.35 minutes are provided by the table. The values we will use are: - Propionaldehyde: - Concentration at 11.12 min: 0.0346 M - Concentration at 40.35 min: 0.0242 M - HCN: - Concentration at 11.12 min: 0.0619 M - Concentration at 40.35 min: 0.0515 M

Step 2: Calculating the average rate of consumption of HCN.

We are asked to find the average rate of consumption of HCN between 11.12 minutes and 40.35 minutes. We will use the formula for average rate of consumption: Average rate of consumption = \(\frac{\text{Change in concentration}}{\text{Change in time}}\) Inserting the values for HCN: Average rate of consumption = \(\frac{0.0619 \, \text{M} - 0.0515\, \text{M}}{40.35 \, \text{min}- 11.12 \, \text{min}}\) Average rate of consumption = \(\frac{0.0104\, \text{M}}{29.23\, \text{min}}\) Average rate of consumption = \(3.56 \times 10^{-4}\, \text{M/min}\) The average rate of consumption of HCN between 11.12 minutes and 40.35 minutes is \(3.56 \times 10^{-4} \, \text{M/min}\).

Step 3: Calculating the average rate of consumption of propionaldehyde.

We are asked to find the average rate of consumption of propionaldehyde between 11.12 minutes and 40.35 minutes. We will again use the formula for average rate of consumption: Average rate of consumption = \(\frac{\text{Change in concentration}}{\text{Change in time}}\) Inserting the values for propionaldehyde: Average rate of consumption = \(\frac{0.0346\, \text{M} - 0.0242\, \text{M}}{40.35\, \text{min} - 11.12 \, \text{min}}\) Average rate of consumption = \(\frac{0.0104\, \text{M}}{29.23\, \text{min}}\) Average rate of consumption = \(3.56 \times 10^{-4}\, \text{M/min}\) The average rate of consumption of propionaldehyde between 11.12 minutes and 40.35 minutes is \(3.56 \times 10^{-4}\, \text{M/min}\). To summarize, the average rate of consumption of HCN between 11.12 minutes and 40.35 minutes is \(3.56 \times 10^{-4}\, \text{M/min}\) and the average rate of consumption of propionaldehyde during the same period is also, \(3.56 \times 10^{-4}\, \text{M/min}\).

Key Concepts

Average Rate of Reaction

When we talk about the average rate of reaction, we're discussing how fast a chemical reaction occurs over a certain period. The rate of reaction is all about the change in concentration of a reactant or a product as time goes on. To find the average rate, we simply divide the change in concentration by the time over which the reaction occurs.

For example, in the reaction involving propionaldehyde and hydrocyanic acid, we use the formula:

• Average rate of consumption = \( \frac{\text{Change in concentration}}{\text{Change in time}} \)

This tells us how quickly the reactants are being used up. When the concentration decreases over time, it indicates that the reactants are being consumed. We frequently use Molarity (M), which is moles per liter, to express concentrations in these calculations.

Understanding the average rate is crucial because it gives chemists and scientists insight into how a reaction progresses and allows them to compare different reactions' speeds.

Consumption of Reactants

During a chemical reaction, reactants are converted into products, and their concentrations decrease over time. This decrease is what we call the "consumption of reactants." To quantify this consumption, we calculate the average rate of consumption — a measure of how fast the reactants disappear.

Let's consider the case of hydrocyanic acid and propionaldehyde. From the exercise, we determine:

• For hydrocyanic acid (HCN), the concentration dropped from 0.0619 M to 0.0515 M from 11.12 min to 40.35 min.
• For propionaldehyde, the concentration decreased from 0.0346 M to 0.0242 M over the same period.

Both reactants showed the same average rate of consumption, which was calculated as \(3.56 \times 10^{-4} \text{ M/min}\).

Understanding how reactants are consumed helps in optimizing conditions for industrial processes or ensures safety in chemical reactions. Knowledge of consumption rates can also aid in predicting the reaction's completion time.

Propionaldehyde and Hydrocyanic Acid Reaction

The reaction between propionaldehyde and hydrocyanic acid takes place in an aqueous solution and provides us a classic example of a chemical process where reactants are gradually consumed to form products. This reaction was studied at a temperature of \(25^{\circ} \text{C}\).

To understand the kinetics of this reaction, let's look at how the concentrations of the reactants changed over time. In this reaction:

• Propionaldehyde (\(\text{CH}_3\text{CH}_2\text{CHO}\)) and hydrocyanic acid (HCN) serve as the primary reactants.
• Concentrations of both decreased over the measuring period, providing clear evidence of their consumption in the reaction.

An interesting observation from the exercise data was that the rates of consumption were identical for both reactants. This might indicate a balanced stoichiometry or a consistent mechanism in which these substances react.

Investigating such reactions provides an insight into fundamental principles of chemical kinetics and allows an empirical approach to understand how different factors affect the speed of reactions.