Problem 20 - Chemistry: Principles and Reactions

Question

The decomposition of ammonia on tungsten at \(1100^{\circ} \mathrm{C}\) is zero- order with a rate constant of \(2.5 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min} .\) (a) Write the rate expression. (b) Calculate the rate when \(\left[\mathrm{NH}_{3}\right]=0.075 M\). (c) At what concentration of ammonia is the rate equal to the rate constant?

Step-by-Step Solution

Answer

Answer: The rate expression for a zero-order reaction is Rate = k, where k is the rate constant. In this case, the rate does not depend on the concentration of ammonia or any other reactants. Therefore, the rate of the reaction will always be equal to the rate constant, regardless of the concentration of ammonia.

Step 1: (a) Rate expression for a zero-order reaction

A zero-order reaction has a rate that depends on the rate constant but does not depend on the concentration of the reactants. The general rate expression for a zero-order reaction is given by: Rate = k In this case, k is the rate constant.

Step 2: (b) Calculate the rate when \([\mathrm{NH}_{3}] = 0.075 M\)

For a zero-order reaction, the rate does not depend on the concentration of the reactants. Since we are given the rate constant \(k = 2.5 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min}\), the rate is equal to the rate constant, irrespective of the concentration of NH3. So the rate of the reaction is: Rate = k = \(2.5 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min}\)

Step 3: (c) Concentration of ammonia when the rate equals the rate constant

Since the rate is equal to the rate constant k for a zero-order reaction, the concentration of NH3 does not affect the rate. Therefore, the rate of the reaction will always be equal to the rate constant, regardless of the concentration of ammonia.

Key Concepts

Rate Expression

In chemical kinetics, the term rate expression describes the relationship between the rate of a chemical reaction and the concentrations of reactants. When it comes to a zero-order reaction, the rate expression takes a uniquely simple form. Unlike first-order or second-order reactions, where the rate depends on the concentration of the reactants raised to the power of one or two, respectively, the rate of a zero-order reaction is constant.

In mathematical terms, the rate expression for a zero-order reaction is simply: \[\text{Rate} = k\] where \(k\) is the rate constant. This implies that the rate is independent of the concentration of the reactants; it will remain constant as long as the reactant is present. This is a critical point of understanding for students, as it significantly simplifies calculations involving zero-order kinetics.

Reaction Rate

The reaction rate is a measure of how quickly a reactant is consumed or a product is formed in a chemical reaction. For a zero-order reaction, the rate is constant and is equal to the rate constant, \(k\). This means that no matter the concentration of reactant present, as long as some reactant remains, the reaction will proceed at a consistent speed.

In the context of the solved exercise, the reaction rate for the decomposition of ammonia on tungsten is \(2.5 \times 10^{-4} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{min}\), which remains constant despite the initial concentration of ammonia. It's important for students to recognize that this is a characteristic of zero-order kinetics and will not apply in reactions of other orders.

Chemical Kinetics

The field of chemical kinetics involves studying and understanding the rates of chemical reactions and the factors influencing them. This includes analyzing how different conditions such as concentration, temperature, and catalysts impact the speed at which reactions occur. Kinetics is pivotal for predicting the behavior of chemicals in various settings, from industrial processes to biological systems.

With regard to zero-order reactions, a key point is that the rate is unaffected by varying concentrations of reactants. Instead, zero-order reaction rates can be influenced by other factors like temperature and the presence of catalysts. This was exemplified in the decomposition of ammonia in the exercise, where the reaction occurred on a tungsten surface at a high temperature. These conditions collectively define the rate constant and subsequently, the steady rate of the reaction.