Question

For a particular reaction at 215.7 °C, ΔG = 404.91 kJ/mol, and ΔS = 748.20 J/(mol·K).

Calculate delta G for -74.3 celcius.

I've asked this question previously and the individual who answered got roughly 378 kj/mol which is incorrect.

Answer 1

delta G = delta H - (T*delta S)

First calculate the delta H as follows:

delta H= delta G - (T*delta S)

Here T = 215.7 °C or 488.7 K, ΔG = 404.91 kJ/mol or 404910 J/mol ΔS = 748.20 J/(mol·K).

delta H= 404910 J/mol - ((488.7K)*(748.20/( J/(mol·K)

delta H = 404910 J/mol -365645.34 J/ mol

= 39264.66 J/mol or 39.26 kj/mol

First calculate the k at T1=215.7 °C or 488.7 K temperature as follows:

404910 J/mol = - 8.3145 *488.7 K lnk1

lnk=-0.01

k1 = 0.99

Now determine k at T2= -74.3 celcius or 198.7 K

ln(K2/K1) = (delta H/R)* [1/T1 - 1/T2]

ln(K2- ln 0.99) = (39264.66 J/mol /8.3145 )* [1/488.7 - 1/198.7]

ln(K2- ln 0.99) = (39264.66 J/mol /8.3145 )*2.04*10^-3-5.03*10^-3

ln(K2- ln 0.99) = (39264.66 J/mol /8.3145 )*-2.99*10^-3

ln(K2+0.01) = -14.13

ln k = -14.14

k= 7.2*10^-7

Now we use, delta G^0 = - RTlnk

delta G^0 = - 8.3145*197.7 *ln 7.2*10^-7

delta G^0 = - 8.3145*197.7 *-14.14

delta G^0 = +23243.00 J/mol

delta G^0 = +23.24 k J/mol