A first order reaction has a half-life period of 69.3sec At 0.10mol/l reactant concentration the rate with ll be

To find the rate of a first-order reaction when given the half-life and the concentration of the reactant, we can use the relationship between the half-life and the rate constant, as well as the definition of rate for a first-order reaction.

Understanding First-Order Reactions

In a first-order reaction, the rate depends linearly on the concentration of one reactant. The rate can be expressed with the equation:

• Rate = k [A]

where k is the rate constant and [A] is the concentration of the reactant.

Half-Life of First-Order Reactions

For first-order reactions, the half-life is a constant that is independent of the initial concentration of the reactant. The formula for the half-life (t_1/2) is given by:

• t_1/2 = 0.693 / k

From the information provided, the half-life is 69.3 seconds. We can rearrange the formula to solve for the rate constant k:

Calculating the Rate Constant

Rearranging the half-life equation gives:

• k = 0.693 / t_1/2

Substituting the given half-life:

• k = 0.693 / 69.3 s
• k ≈ 0.01 s^-1

Finding the Reaction Rate

Now that we have the rate constant k, we can find the rate of the reaction at the given concentration of 0.10 mol/L:

• Rate = k [A]
• Rate = 0.01 s^-1 × 0.10 mol/L
• Rate = 0.001 mol/L·s

Summary of Findings

Thus, the rate of the first-order reaction at a reactant concentration of 0.10 mol/L is 0.001 mol/L·s. This exemplifies how the rate of a reaction can be calculated using the half-life and concentration of the reactant, showcasing the predictable nature of first-order kinetics.