Chemical kinetics is the study of how fast chemical reactions occur and what factors affect their rates. One of the important concepts in chemical kinetics is the relationship between the rate of formation of products and the rate of disappearance of reactants in a balanced chemical equation.

In this article, we will explore how to express this relationship for a simple reaction involving water and oxygen, and how to use it to calculate the rates of different species.

Contents

## The reaction of hydrogen and oxygen

The reaction of hydrogen and oxygen to form water is one of the most common and important reactions in chemistry. It can be written as:

$$2H_2(g) + O_2(g) \rightarrow 2H_2O(g)$$

This reaction is exothermic, meaning that it releases heat, and can be used as a source of energy in fuel cells or rockets.

The rate of formation and disappearance

The rate of a chemical reaction is defined as the change in concentration of a reactant or product per unit time. For example, the rate of formation of water in this reaction is:

$$\text{Rate of formation of water} = \frac{\Delta[H_2O]}{\Delta t}$$

where $\Delta[H_2O]$ is the change in concentration of water and $\Delta t$ is the change in time.

Similarly, the rate of disappearance of oxygen in this reaction is:

$$\text{Rate of disappearance of oxygen} = -\frac{\Delta[O_2]}{\Delta t}$$

where $\Delta[O_2]$ is the change in concentration of oxygen and $\Delta t$ is the change in time. The negative sign indicates that the concentration of oxygen decreases as the reaction proceeds.

## The stoichiometric relationship

The balanced chemical equation tells us how many moles of each reactant or product are involved in the reaction. For example, for every 2 moles of hydrogen that react, 1 mole of oxygen reacts and 2 moles of water are formed. This means that the rates of formation and disappearance are related by a stoichiometric factor that depends on the coefficients in the equation. For this reaction, we can write:

$$-\frac{\Delta[O_2]}{\Delta t} = \frac{1}{2}\frac{\Delta[H_2O]}{\Delta t}$$

or

$$\frac{\Delta[H_2O]}{\Delta t} = 2 \times (-\frac{\Delta[O_2]}{\Delta t})$$

This equation tells us that the rate of disappearance of oxygen is half the rate of formation of water, or equivalently, that the rate of formation of water is twice the rate of disappearance of oxygen.

## How to use this relationship

This relationship can be useful for calculating the rates of different species if we know the rate of one species. For example, if we measure that the rate of formation of water at a certain instant is $4.0 \times 10^{-5}$ M/s, we can use this equation to find the rate of disappearance of oxygen at that instant:

$$-\frac{\Delta[O_2]}{\Delta t} = \frac{1}{2}\frac{\Delta[H_2O]}{\Delta t} = \frac{1}{2} \times (4.0 \times 10^{-5}) = 2.0 \times 10^{-5} M/s$$

This means that at that instant, the concentration of oxygen is decreasing by $2.0 \times 10^{-5}$ M/s.

Alternatively, if we measure that the rate of disappearance of oxygen at a certain instant is $-6.0 \times 10^{-5}$ M/s, we can use this equation to find the rate of formation of water at that instant:

$$\frac{\Delta[H_2O]}{\Delta t} = 2 \times (-\frac{\Delta[O_2]}{\Delta t}) = 2 \times (-6.0 \times 10^{-5}) = 1.2 \times 10^{-4} M/s$$

This means that at that instant, the concentration of water is increasing by $1.2 \times 10^{-4}$ M/s.

## Conclusion

In this article, we have learned how to express the relationship between the rate of formation of water and the rate of disappearance of oxygen in a simple reaction involving hydrogen and oxygen. We have also seen how to use this relationship to calculate the rates of different species if we know the rate of one species. This is a basic skill in chemical kinetics that can help us understand and control the speed of chemical reactions.