Question

Zinc metal dissolves in hydrochloric acid according to the reaction $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q)-\ldots \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ 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.

Short answer

To design an experimental apparatus for monitoring the partial pressure of hydrogen gas, we can use a reaction flask containing zinc and hydrochloric acid connected to a gas syringe to measure the volume of hydrogen gas produced. To determine the rate law, reaction order for H+ ions, activation energy, and the effect of changing the form of Zn from metal strips to granules, we need to perform a series of experiments. For each experiment, we vary the initial concentrations of reactants, temperature, and the form of zinc, and measure the rate of hydrogen gas production. This information is used to construct plots, analyze the data, and determine the desired information, such as reaction order and activation energy, based on the observed trends.

Step-by-step solution

(a) Designing the experimental apparatus

To monitor the partial pressure of hydrogen gas produced, we can set up an apparatus with a gas syringe or burette connected to the top of a reaction flask containing zinc and hydrochloric acid. Initially, the flask is closed, so when the reaction begins, it pushes the plunger of the syringe out as the pressure inside increases due to the hydrogen gas production.

(b) Determining the rate law of the reaction

To determine the rate law of the reaction, we can measure the amount of hydrogen gas produced at different time intervals. We can plot this data as a function of time, and by measuring the initial rate of the reaction (the slope of the tangent at the beginning of the curve), we can determine the rate constant. We can also determine the order of the reaction with respect to the reactants by varying their initial concentrations and observing their effect on the initial rate of the reaction.

(c) Determining the reaction order for H+ ions

To determine the reaction order for H+ ions, we can perform a series of experiments with differing initial concentrations of hydrochloric acid, while keeping the concentration of zinc constant. By analyzing the changes in the initial rates, we can determine the reaction order for H+ ions. The reaction order would be the exponent value in the rate law that best fits the observed data.

(d) Determining the activation energy of the reaction

To determine the activation energy of the reaction, we can perform a series of experiments at different temperatures while measuring the rate of hydrogen gas production at each temperature. By plotting the natural logarithm of the reaction rate versus the inverse of the temperature (\( 1/T\)), we can use the Arrhenius equation, \[ \ln (k)=-\frac{E_{a}}{R} \cdot \frac{1}{T}+\ln (A), \] where k is the rate constant, Ea is the activation energy, R is the gas constant, T is the temperature in Kelvin, and A is the pre-exponential factor. The slope of the linear plot would be \(-\frac{E_{a}}{R}\); thus, the activation energy can be calculated.

(e) Determining the effects of changing the form of Zn from metal strips to granules

We can perform experiments with both zinc metal strips and granules, while maintaining the same mass and initial concentrations of reactants. By measuring the rate of hydrogen gas production for each form of zinc and comparing the results, we can determine the effect of changing the form of Zn. It is anticipated that the granules will react faster than the strips due to the larger surface area available for the reaction.

Key concepts

Rate of Reaction

Understanding the rate of reaction is key in chemical kinetics. It refers to how quickly a reactant is consumed or a product is formed. For the reaction between zinc and hydrochloric acid, measuring the production of hydrogen gas over time gives us insight into this rate. We can monitor the rate by tracking changes in pressure or volume in a closed system. This involves recording data at various time intervals. Plotting the concentration of hydrogen over time yields a curve that can help determine the reaction rate. Rates usually depend on factors like concentration and temperature, which makes studying them crucial for predicting how reactions proceed.

Reaction Order

Reaction order indicates the power to which the concentration of a reactant is raised in the rate law. To find this for the reaction between zinc and hydrochloric acid, we vary the concentration of hydrochloric acid while keeping the zinc constant. Observing changes in reaction rate reveals the order with respect to the hydrogen ions. For example, if doubling the acid concentration approximately doubles the reaction rate, the reaction is first order in \( \ ext{H}^+ \). Calculations typically require analysis of experimental data to fit a suitable mathematical model that aligns with the rate law for the reaction.

Activation Energy

Activation energy is the energy needed to start a reaction. It's a crucial factor that determines the rate at which a reaction proceeds. We can determine it experimentally by measuring the reaction rate at various temperatures. Using the Arrhenius equation, plotting \( \ln(k) \) against \( 1/T \) creates a linear graph. The slope of this graph is related to the activation energy. A low activation energy usually means a reaction proceeds quickly, while a high activation energy means it proceeds slowly. Understanding activation energy allows chemists to control reaction conditions to optimize rates effectively.

Experimental Apparatus

Designing the right experimental apparatus is pivotal for accurate measurements. In this experiment, a reaction flask equipped with a gas syringe measures the hydrogen gas produced. The flask is initially closed. As zinc reacts with hydrochloric acid, hydrogen gas generates pressure, moving the syringe plunger. Using a manometer can also help monitor pressure changes easily. This setup provides a straightforward way to capture data on reaction rates. Ensuring airtight connections and stable temperature conditions is critical for reliable results. This setup helps reduce errors and improves data accuracy.

Gas Collection Methods

Proper gas collection methods are essential in studying reactions that produce gases like hydrogen. Using a syringe or a burette to collect the gas is excellent for reactions like zinc and hydrochloric acid. These methods directly measure the volume of gas formed, offering precise quantitative analysis. Additionally, performing the reaction in a way that allows the gas to be funneled through a drying tube can remove moisture, leading to more accurate results. Understanding the best technique for gas collection helps in deriving meaningful conclusions from the data obtained, particularly when dealing with gases that can easily escape or get absorbed.