Problem 106 - Chemistry: The Central Science

Question

Zinc metal dissolves in hydrochloric acid according to the reaction $$ \mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(a q)--\rightarrow \operatorname{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ Suppose you are asked to study the kinetics of this reaction by monitoring the rate of production of \(\mathrm{H}_{2}(g)\). (a) By using a reaction flask, a manometer, and any other common laboratory equipment, design an experimental apparatus that would allow you to monitor the partial pressure of \(\mathrm{H}_{2}(g)\) produced as a function of time. (b) Explain how you would use the apparatus to determine the rate law of the reaction. (c) Explain how you would use the apparatus to determine the reaction order for \(\left[\mathrm{H}^{+}\right]\) for the reaction. (d) How could you use the apparatus to determine the activation energy of the reaction? (e) Explain how you would use the apparatus to determine the effects of changing the form of \(\mathrm{Zn}(s)\) from metal strips to granules.

Step-by-Step Solution

Answer

(a) Design an apparatus consisting of a reaction flask, a manometer, a burette, a stopwatch, and a data logging system. (b) Perform the experiment at different initial concentrations of hydrochloric acid, monitor the partial pressure of \(H_2(g)\), and analyze the data to find the rate law. (c) Determine the reaction order for \([\mathrm{H}^{+}]\) by analyzing the relationship between the initial rate and the initial concentration of hydrochloric acid. (d) Perform the experiment at different temperatures, determine the rate constant, and use slope value from the Arrhenius plot to calculate the activation energy. (e) Compare the results of experiments using both metal strips and granules of zinc to analyze the difference in reaction rates and its causes.

Step 1: Apparatus Components

To monitor the partial pressure of \(H_2(g)\) produced as a function of time, the experimental setup will require a reaction flask, a manometer, a burette, a stopwatch, a data logging system, and common laboratory equipment such as clamp stands and beakers. A suitable setup would consist of the following components: 1. A reaction flask with a ground-glass joint for the introduction of hydrochloric acid. 2. A one-hole stopper fitted with a gas-tight connector for the manometer in the flask's mouth to measure the pressure of the hydrogen gas produced. 3. A burette filled with hydrochloric acid to control the flow and amount of acid added to the reaction flask. 4. A stopwatch to measure the time. 5. A data logging system/software to record the measurements. (b) Determine the rate law

Step 2: Perform the Experiment

Determine the rate law by performing the experiment at different initial concentrations of hydrochloric acid while maintaining the mass of zinc constant. Monitor and record the partial pressure of \(H_2(g)\) produced in the manometer as a function of time. Repeat the experiment for each set of initial concentrations and note the time for each.

Step 3: Calculations

Calculate the initial rate of the reaction using the rate of production of \(H_2(g)\) for each experiment. Plot the initial rate versus the initial concentration of hydrochloric acid for each data set and analyze the data to find the rate law of the reaction. (c) Determine the reaction order for [H+]

Step 4: Evaluate Reaction Order

To determine the reaction order for \([\mathrm{H}^{+}]\), analyze the data from the previous step. Study the plot of the initial rate versus the initial concentration of hydrochloric acid and look for the relationship between them. The reaction order concerning \([\mathrm{H}^{+}]\) will be determined by the exponent in the rate law equation involving the initial concentration of hydrochloric acid. (d) Determine the activation energy

Step 5: Temperature Control

To determine the activation energy, first perform the experiment using different initial concentrations of hydrochloric acid, as described in step (b), but at different controlled temperatures.

Step 6: Arrhenius Plot

For each temperature, determine the rate constant, \(k\), from the experiment. Next, plot ln(k) versus 1/Temperature on a graph called the Arrhenius plot. The slope of the straight line in this plot will be equal to \(-E_a/R\), where \(E_a\) is the activation energy, and \(R\) is the gas constant. Calculate \(E_a\) using the slope value. (e) Determine the effects of changing the form of Zn(s) from metal strips to granules

Step 7: Perform Experiments

Perform the experiment as described in step (b) using both metal strips and granules of zinc while keeping other parameters constant.

Step 8: Compare Results

Compare the results obtained from both forms of zinc (strips and granules) by comparing the initial rates of the reaction and the rate law for each form. Analyze the difference in reaction rates, which could be attributed to changes in surface area and mass transport effects.

Key Concepts

Reaction Rate Law Determination

Understanding the rate law of a chemical reaction is essential for grasping the kinetics behind it. It provides information on how the rate of reaction is affected by the concentration of reactants. To determine the rate law for the reaction between zinc and hydrochloric acid, we would conduct experiments varying the concentration of hydrochloric acid, measuring how fast hydrogen gas is produced.

By plotting the initial rates of reaction against the corresponding concentrations of hydrochloric acid, we can establish a mathematical relationship. The resulting graph would indicate whether the reaction rate is directly proportional to the concentration of the reactants, and if so, to what degree – demonstrating the order of the reaction with respect to hydrochloric acid.

Arrhenius Equation

The Arrhenius equation is a mathematical expression that describes how the rate of a chemical reaction changes with temperature. According to this equation, reaction rates increase exponentially with an increase in temperature. However, for this to occur, molecules must exceed a minimal energy threshold known as the activation energy.

By running the zinc and hydrochloric acid reaction at various temperatures and calculating the rate constants for these temperatures, we can create an Arrhenius plot.

Arrhenius Plot Analysis

This is a graph of the natural logarithm of the rate constant, \( ln(k) \), plotted against the inverse of the absolute temperature, \( 1/T \). The negative slope of the line on this graph is directly proportional to the activation energy, providing us with a clear path to determine this crucial value.

Activation Energy Calculation

The activation energy of a reaction is the energy barrier that must be overcome by the reactants to result in a successful chemical reaction. To determine the activation energy for the reaction where zinc dissolves in hydrochloric acid, we would utilize the Arrhenius equation and the data obtained from our experiments at different temperatures.

The slope derived from the linear Arrhenius plot is used in the equation \( E_a = -R \times slope \) where \( R \) is the universal gas constant, to calculate the activation energy (\( E_a \)). This calculation gives us insights into how easily a reaction occurs – lower activation energies mean that the reaction is more likely to proceed at a given temperature.

Zinc and Hydrochloric Acid Reaction

When zinc metal is introduced to hydrochloric acid, a notable reaction occurs, with zinc dissolving to form zinc chloride and hydrogen gas being released. To study the effect of the physical form of zinc on this reaction, we can compare how zinc strips and zinc granules react with hydrochloric acid under controlled conditions.

Differing surface areas between strips and granules can lead to variations in reaction rate. If done correctly, this experiment can demonstrate the influence of surface area and morphology on chemical kinetics, as granules provide a higher surface area and often result in increased reaction rates when the mass and other conditions are kept constant.