Question

The reaction:
A → B + C

is known to be second order with respect to A and to have a rate constant of 0.00255 M^-1 s^-1 at 285 K. It is also known that ΔG^o_rxn for this reaction is -2.13 kJ.

An experiment was run at this temperature where only reactants were present ([A]_o = 0.331 M). Calculate ΔG_nonstandard after 14.1 seconds has elapsed.

Answer 1

R = k [A]^2

Second order rate law :

1/At = 1/Ao + kt

At = concentration after time t

Ao = initial concetration

k = rate constant and t = time

At at time = 14.2 seconds

1/At = 1/0.331 + (0.00255*14.1)

At = 0.3271 M

A    ------> B + C

0.331        0       0

0.331-x     x       x

At = 0.331-x = 0.3271

x = 0.0039 M

[B] = [C] = 0.0039 M

delta Gnon = delta Go + RT * lnQ

Q = [B]*[C] / [A] = [0.0039] * [0.0039] / [0.3271] = 4.65*10^-5

delta Gnon = -2.13*1000 + (8.314*285) * ln (4.65*10^-5 )

delta Gnon = -25.768 KJ