# Rate Law for IBr Decomposition: Explained Step-by-Step

• jupiter_8917
In summary: It is important to realize that k' is not equal to k. In summary, the rate law for the proposed mechanism of the decomposition of IBr to I2 and Br2 is R=k[IBr]^2. This is derived from the fact that the rate of the reaction is dependent on the slowest step in the mechanism, which in this case is the 2nd step. We also replace [Br] with h[IBr] to eliminate the intermediate in the rate equation, resulting in the modified rate constant k'.

#### jupiter_8917

Write the rate law for the following proposed mechanism for the decomposition of IBr to I2 and Br2.

IBr(g)---------->I(g) + Br(g) (fast)
IBr(g) + Br(g)-------->I(g) + Br2(g) (slow)
I(g) + I(g)--------->I2(g) (fast)

The answer is R=k[IBr]^2. I don't know where this answer comes from. Can anyone please explain it to me step by step? Thank you for your help!

We know that for an elementary reaction step, the rate is proportional to the product of the molar concentrations of each reactant.
For a reaction with a multi-step mechanism, the rate of the reaction is dependent on the rate of limiting step ie the slowest step. In this case here it is the 2nd step. So, we have a preliminary rate equation:
$$rate = k[IBr][Br]$$​

However, it does not make any sense to have an intermediate in the rate equation, so we replace [Br] with the reactant(s) that form it. Since the reaction IBr(g)----->I(g) + Br(g) occurs rapidly, [Br] is clearly a fraction of [IBr]. And thus we replace [Br] with h[IBr] where h is a constant to obtain
$$rate = k'[IBr]^2$$​
where k' denotes a modified rate constant.

## 1. What is the rate law for IBr decomposition?

The rate law for IBr decomposition is a mathematical expression that shows the relationship between the concentration of reactants and the rate of the reaction. It is given by the equation: Rate = k[IBr]^m[H2]^n, where k is the rate constant, [IBr] and [H2] are the concentrations of IBr and H2 respectively, and m and n are the reaction orders for IBr and H2.

## 2. How is the rate constant determined in the rate law for IBr decomposition?

The rate constant, k, is determined experimentally by measuring the initial rate of the reaction at different concentrations of reactants and then using these values to calculate the rate constant. It can also be determined by using the integrated rate law and the half-life of the reaction.

## 3. What is the significance of the reaction orders in the rate law for IBr decomposition?

The reaction orders, m and n, in the rate law indicate the dependence of the reaction rate on the concentration of each reactant. A reaction order of 0 indicates no effect on the rate, 1 indicates a direct proportionality, and 2 indicates a squared dependence on the concentration.

## 4. Can the rate law for IBr decomposition be used to predict the rate of the reaction at any given concentration?

Yes, the rate law can be used to predict the rate of the reaction at any given concentration of reactants. However, it is important to note that the rate constant, k, may change with temperature and the rate law must be determined experimentally for each set of reaction conditions.

## 5. How does the rate law for IBr decomposition relate to the overall reaction mechanism?

The rate law is determined by the slowest step in the reaction mechanism, known as the rate-determining step. The concentrations of the reactants in the rate law correspond to the concentrations of the reactants involved in the rate-determining step. Therefore, the rate law provides insight into the steps and intermediates involved in the overall reaction mechanism.