Question

A first order reaction is 35% complete in 10s (35% of the reactants were converted into products). What is the rate constant and half-life?

a) k = 0.1 s⁻¹, t1/2 = 6.93s
b) k = 0.07 s⁻¹, t1/2 = 10s
c) k = 0.05 s⁻¹, t1/2 = 13.86s
d) k = 0.2 s⁻¹, t1/2 = 5s

Answer 1

The rate constant for the first-order reaction is approximately 0.072 s⁻¹, and the half-life is approximately 9.61s.

Step-by-step explanation:

A first-order reaction is 35% complete in 10s (35% of the reactants were converted into products). To find the rate constant of the reaction, we can use the equation for the integrated rate law of a first-order reaction: ln(Rt/R0) = -kt, where Rt is the concentration of the reactant at time t, R0 is the initial concentration of the reactant, k is the rate constant, and t is the time. Since the reaction is 35% complete, the concentration of the reactant at 10s is 65% of the initial concentration. Substituting these values into the equation and solving for k, we find that k = -ln(0.65)/10s. This gives us a rate constant of approximately 0.072 s⁻¹.

To find the half-life of the reaction, we can use the equation for the half-life of a first-order reaction: t1/2 = 0.693/k. Substituting the value of k we found earlier, we calculate the half-life to be approximately 9.61s.