Answer to Question #316524 in Physical Chemistry for Peter

Question

For a certain first order reaction, half life is 100s, how long will it take to be 75% completed

Answer 1

t_1/2 = 100 s;

t_1/2 = ln(2)/k;

k = ln(2)/t_1/2 = 0.693/100 = 0.00693 s^-1;

[C_t]/[C₀] = e^-k*t;

ln([C_t]/[C₀]) = -k*t;

k = -(ln([C_t]/[C₀]))/t;

t = -(ln([C_t]/[C₀]))/k = ln([C₀]/[C_t])/k = ln(x/(x-0.75x))/k = ln(x/0.25x)/k = ln(4)/0.00693 = 200 s.

Answer: 200 s.