Question

The following statements relate to the reaction for the formation of HI: $$\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{HI}(\mathrm{g}) \quad \text { Rate }=k\left[\mathrm{H}_{2}\right]\left[\mathrm{I}_{2}\right]$$ Determine which of the following statements are true. If a statement is false, indicate why it is incorrect. (a) The reaction must occur in a single step. (b) This is a second-order reaction overall. (c) Raising the temperature will cause the value of \(k\) to decrease. (d) Raising the temperature lowers the activation energy for this reaction. (e) If the concentrations of both reactants are doubled, the rate will double. (f) Adding a catalyst in the reaction will cause the initial rate to increase.

Short answer

(b) is true and (f) is true. All other statements are false.

Step-by-step solution

Identify Reaction Order

Given the rate law \(\text{Rate} = k[\text{H}_2][\text{I}_2]\), identify the order of the reaction with respect to each reactant. The reaction is first-order with respect to \(\text{H}_2\) and first-order with respect to \(\text{I}_2\). Therefore, the overall order of the reaction is the sum of the exponents, \(1 + 1 = 2\). Thus, it is a second-order reaction.

Review Statement (a)

Statement (a) claims the reaction must occur in a single step. A reaction's molecularity (single-step mechanism) cannot be determined just from the rate law. Therefore, statement (a) is false because the reaction could be a multi-step process.

Review Statement (b)

Since the overall reaction order is determined to be 2, statement (b) is true.

Review Statement (c)

Statement (c) states raising the temperature causes the value of \(k\) to decrease. In general, increasing temperature increases the rate constant \(k\) for most reactions, according to the Arrhenius equation. Therefore, statement (c) is false.

Review Statement (d)

Statement (d) suggests that raising the temperature lowers the activation energy. Instead, raising the temperature does not change the activation energy but provides more thermal energy to surpass it. Thus, statement (d) is false.

Review Statement (e)

Statement (e) claims that doubling concentrations of both reactants will double the rate. For the second-order reaction \(\text{Rate} = k[\text{H}_2][\text{I}_2]\), if both concentrations are doubled, the rate increases by a factor of 4 (\(2 \times 2 = 4\)). Thus, statement (e) is false.

Review Statement (f)

Statement (f) claims adding a catalyst will increase the initial rate. A catalyst provides an alternative pathway with a lower activation energy, typically increasing the rate of reaction. Thus, statement (f) is true.

Key concepts

Reaction Order

The order of a reaction is a crucial concept in chemical kinetics. It tells us how the concentration of reactants affects the rate of the reaction. In a rate law, the order with respect to a particular reactant is the exponent of its concentration term.
For example, when given that the rate law of a reaction is \( \text{Rate} = k[\text{H}_2][\text{I}_2] \), the reaction is first-order with respect to \( \text{H}_2 \) and first-order with respect to \( \text{I}_2 \). The overall order is the sum of the exponents, which in this case is 2.
This makes it a second-order reaction. This means the rate depends on the square of the concentrations of the reactants. If the concentrations are changed, the rate changes significantly.

• A first-order reaction means the rate is proportional to the concentration.
• A second-order reaction means the rate is proportional to the square of the concentration.

Rate Law

The rate law of a chemical reaction is an expression that relates the rate of reaction to the concentrations of the reactants. It is an equation that captures how these concentrations influence the speed at which a reaction proceeds.
The rate law is generally given by: \( \text{Rate} = k[A]^m[B]^n \), where \( k \) is the rate constant, \( A \) and \( B \) are reactants, and \( m \) and \( n \) are the orders of the reaction with respect to each reactant.
If we take our example, \( \text{Rate} = k[\text{H}_2][\text{I}_2] \), each reactant's exponent reflects its effect on the rate. In many cases, the overall order of the reaction (sum of individual orders) helps determine how changes in concentration will impact the reaction rate.

• The rate constant \( k \) is specific to a reaction at a given temperature.
• Larger exponents indicate a more significant effect on the reaction rate.

Activation Energy

Activation energy is the minimum energy that reactants need to start a chemical reaction. It's an energy barrier that reactants must overcome to transform into products.
With the help of a graph, called a reaction energy diagram, you can see activation energy as the peak that needs to be surpassed to get from reactants to products.
One important idea in kinetics is that raising the temperature does not lower the activation energy itself. Instead, it provides the reactants with more energy to help surpass that barrier. An increase in temperature usually reduces the time it takes for particles to reach that energy level, thus speeding up the reaction.

• More thermal energy makes it easier to overcome the activation energy.
• The activation energy is specific for each reaction.

Catalyst Effect

A catalyst plays a fascinating role in chemical reactions. It speeds up a reaction by providing an alternative pathway with a lower activation energy. This means the energy peak that reactants need to overcome is lower, making it easier for them to convert into products.
Importantly, a catalyst is not consumed in the reaction; it is available to participate in the reaction cycle repeatedly. By lowering the activation energy, a catalyst increases the rate without altering the overall capacity of the reaction.
This is why adding a catalyst to a reaction typically increases the initial reaction rate, fulfilling its primary purpose. Catalysts are extensively used in many industrial processes to enhance efficiency.

• Catalysts do not change the final products of the reaction.
• They reduce energy costs in industrial processes by lowering the required energy input.