The rate for the decomposition of \(\mathrm{NH}_{3}\) on platinum surface is zero order. What are the rate of production of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) if \(K=2.5 \times 10^{-4}\) mol litre \(^{-1} \mathrm{~s}^{-1}\).

Short Answer

Expert verified
The rate of production of \text{N}_2 is 1.25 \times 10^{-4} \text{ mol litre}^{-1}\text{s}^{-1}, and the rate of production of H2 is 3.75 \times 10^{-4} \text{ mol litre}^{-1}\text{s}^{-1}.

Step by step solution

01

Write the Balanced Chemical Equation

The balanced chemical equation for the decomposition of ammonia (\text{NH}_3) on a platinum surface is:\[ 2\text{NH}_3 \rightarrow \text{N}_2+3\text{H}_2. \]This indicates that 2 moles of ammonia decompose to form 1 mole of nitrogen and 3 moles of hydrogen.
02

Express the Rate of Decomposition

Since the reaction is zero order, the rate of decomposition of \text{NH}_3 is constant and is given by the rate constant, \( k \). The rate of decomposition is expressed as:\[ \text{Rate}_{\text{NH}_3} = k = 2.5 \times 10^{-4} \text{ mol litre}^{-1}\text{s}^{-1}. \]
03

Determine the Rate of Production of N2

For every 2 moles of NH3 that decompose, 1 mole of N2 is produced. Therefore, the rate of production of N2 is half the rate of decomposition of NH3:\[ \text{Rate}_{\text{N}_2} = \frac{1}{2} \times \text{Rate}_{\text{NH}_3} = \frac{1}{2} \times 2.5 \times 10^{-4} = 1.25 \times 10^{-4} \text{ mol litre}^{-1}\text{s}^{-1}. \]
04

Determine the Rate of Production of H2

For every 2 moles of NH3 that decompose, 3 moles of H2 are produced. Therefore, the rate of production of H2 is three-halves the rate of decomposition of NH3:\[ \text{Rate}_{\text{H}_2} = \frac{3}{2} \times \text{Rate}_{\text{NH}_3} = \frac{3}{2} \times 2.5 \times 10^{-4} = 3.75 \times 10^{-4} \text{ mol litre}^{-1}\text{s}^{-1}. \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Zero Order Reactions
Understanding zero order reactions is crucial for mastering chemical kinetics, particularly when analyzing reaction rates. In zero order reactions, the rate of reaction is constant and does not depend on the concentration of the reactants involved. Instead, the rate is directly proportional to the rate constant, denoted by 'k'.

This means that, no matter how much reactant you have at the beginning, the substance will always decompose or react at the same fixed rate. For example, if you are looking at the decomposition of a substance on a catalyst's surface, such as ammonia (\text{NH}\(_3\)) on platinum, the reaction will proceed at a steady rate defined by the rate constant 'k'.

One interesting characteristic of zero order reactions is that their rate can be affected by external conditions, like temperature and the presence of a catalyst, but not by changes in concentrations of the reactants. When plotted on a graph, the concentration of reactants will decrease linearly over time, rather than exponentially as seen with other reaction orders.
Rate of Decomposition
The rate of decomposition in a chemical reaction is an important aspect of chemical kinetics, referring to how quickly the reactants break down into products. This rate can be influenced by various factors, including reaction order, temperature, and catalysts.

In the context of a zero order reaction like the decomposition of ammonia on a platinum surface, we can denote the rate of decomposition with the general form Rate = k, where 'k' is the rate constant. Here, since the reaction order is zero, the rate remains unchanged regardless of the concentration of the reacting substance. It's essential to understand that, in this scenario, the rate of decomposition directly translates to the rate of production of products. For instance, as 2 moles of ammonia decompose, we'll see 1 mole of nitrogen and 3 moles of hydrogen produced. This is why knowing the stoichiometry of the reaction is as significant as knowing the rate constant 'k' when determining the individual rates of production for products in a zero-order reaction.
Chemical Kinetics
At the heart of understanding reaction rates lies the field of chemical kinetics, the study of the speed at which chemical processes occur. Its principles help us predict how long a reaction will take and the factors affecting this timescale. Chemical kinetics covers not only the rates of chemical reactions but also delves into the mechanisms by which reactions proceed.

With chemical kinetics, we look at variables like temperature, concentration, surface area, and catalysts, all of which can influence the speed of a reaction. For example, increasing the temperature generally increases the rate, as particles have more energy to collide with sufficient force and proper orientation to react. Likewise, catalysts such as a platinum surface in ammonia decomposition can lower the activation energy barrier, allowing reactions to proceed faster at lower temperatures.

Understanding kinetics is not just about knowing what affects reaction rates, but also quantitatively measuring these rates and being able to manipulate them—skills that are paramount in various applications, from industrial synthesis to environmental control and beyond.

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