Question

Give the individual reaction orders for all substances and the overall reaction order from this rate law: $$ \text { Rate }=k \frac{\left[\mathrm{HNO}_{2}\right]^{4}}{[\mathrm{NO}]^{2}} $$

Short answer

The reaction order for \([\text{HNO}_{2}]\) is 4, for \([\text{NO}]\) is -2, and the overall reaction order is 2.

Step-by-step solution

Identify Reaction Order for [HNO2]

Look at the exponent of \([\text{HNO}_{2}]\) in the rate law \(\text { Rate }=k \frac{\big[\text{HNO}_{2}\big]^{4}}{\big[\text{NO}\big]^{2}}\). The exponent is 4, so the reaction order with respect to \([\text{HNO}_{2}]\) is 4.

Identify Reaction Order for [NO]

Look at the exponent of \([\text{NO}]\) in the rate law. The exponent in the denominator counts as negative, so it is -2, making the reaction order with respect to \([\text{NO}]\) equal to -2.

Calculate Overall Reaction Order

Sum the individual reaction orders for all species involved. For this rate law, the sum is 4 (for \([\text{HNO}_{2}]\)) + (-2) (for \([\text{NO}]\)) = 2. Therefore, the overall reaction order is 2.

Key concepts

Rate Law

The rate law is an equation that links the rate of a chemical reaction to the concentration of the reactants. It provides insight into how the speed of a reaction changes when you alter the concentrations of the substances involved. The general form of a rate law can be written as: \( \text{Rate} = k [A]^m [B]^n \).
In this equation:

• Rate: The speed of the reaction.
• k: The rate constant.
• [A] and [B]: The concentrations of reactants A and B.
• m and n: The reaction orders for A and B.

Understanding the rate law is crucial for comprehending how different factors such as concentration affect the reaction rate.

Individual Reaction Orders

Individual reaction orders indicate the power to which the concentration of each reactant is raised in the rate law. They show how the rate depends on the concentration of specific reactants. In our rate law, \( \text{Rate} = k \frac{[\text{HNO}_2]^4}{[\text{NO}]^2} \), we can determine the individual reaction orders as follows:
The reaction order for \( \text{HNO}_2 \) is 4 because the concentration of \( \text{HNO}_2 \) is raised to the fourth power in the numerator. This means that the rate of reaction increases significantly with an increase in the concentration of \( \text{HNO}_2 \).
Next, the reaction order for \( \text{NO} \) is -2, as the concentration of \( \text{NO} \) is in the denominator and therefore has a negative exponent. This implies that an increase in the concentration of \( \text{NO} \) will decrease the reaction rate. Hence, each reactant's contribution to the overall reaction rate depends on these individual orders.

Overall Reaction Order

The overall reaction order is the sum of the individual reaction orders of all the reactants in the rate law. It gives a broad sense of the reaction's dependence on the concentrations of the reactants.
For our given rate law, \( \text{Rate} = k \frac{[\text{HNO}_2]^4}{[\text{NO}]^2} \):

• The reaction order for \( \text{HNO}_2 \) is 4.
• The reaction order for \( \text{NO} \) is -2.

To find the overall reaction order, we simply add these individual orders:
\( 4 + (-2) = 2 \).
Therefore, the overall reaction order of this reaction is 2. This tells us how the rate of the reaction as a whole responds to changes in the concentrations of the reactants.