For a zero-order reaction 3 X Y , the initial concentration of X is 1.2 M. If the half-life of the reaction is 20 minutes, what is the value of the rate constant k ?

Step-by-step solution

For the zero-order reaction 3 X Y , the rate of reaction is given by: Rate = - 1 3 d[ X ] dt = k - d[ X ] dt = 3k Integrating this equation yields the integrated rate law: [ X ]₀ - [ X ]_t = 3kt At the half-life ( t_ 1/2 = 20 min), the concentration of X drops to half of its initial value: [ X ]_t = 1.2 2 = 0.6 M Substituting the values into the integrated rate law: 1.2 - 0.6 = 3 k 20 0.6 = 60k k = 0.6 60 = 0.01 M min ⁻¹ Using the formula without accounting for the stoichiometric coefficient of 3 leads to the incor