Kinetics: Chemistry 102: concentration problem

Question

The rate of decomposition of PH₃ was studied at 951.00 °C. The rate constant was found to be 0.0595  s^–1.

4PH3​P4​+6H2​

If the reaction is begun with an initial PH₃ concentration of 0.95 M, what will be the concentration of PH₃ after 37.00  s?

Answer 1

From the units of the rate constant, s^-1, we can tell that this is a first order reaction.

The half life of a 1st order reaction is t_1/2 = ln 2 /k = 0.693 / 0.0505 s^-1 = 11.65 s

Now that we know the half life, we can use a simple equation FR = 0.5ⁿ

FR = fraction remaining = ?

n = number of half lives that have elapsed = 37 sec / 11.65 sec = 3.176 half lives

FR = 0.5^3.176

FR = 0.1106

Since we began with 0.95 M the concentration remaining is 0.95 x 0.1106 = 0.105 M = 0.11 M (2 sig. figs.)

You could also do this problem using the integrated rate law for a 1st order reaction:

[A] = [A]_oe^-kt

or ln [A] = -kt + ln[A]_o

ln[A] = -(0.0595)(37) + ln(0.95)

ln[A] = -2.20 + (-0.05)

ln[A] = -2.25

[A] = 0.105 M = 0.11 M