The rate constant k for a first-order reaction can be determined using the half-life t1/2 of the reaction. The relationship between the rate constant and half-life for a first-order reaction is given by the formula:k = ln 2 / t1/2where ln 2 is the natural logarithm of 2 approximately 0.693 and t1/2 is the half-life in the same units as the rate constant in this case, minutes .Given a half-life of 10 minutes, we can calculate the rate constant as follows:k = 0.693 / 10k 0.0693 minSo, the rate constant for this first-order reaction is approximately 0.0693 min. Note that the initial concentration of the reactant 0.1 M is not needed to calculate the rate constant for a first-order reaction.