Calculate ΔG°' for the reaction A + B <-> C + D at 25°C when the equilibrium concentrations are [A] = 10 uM, [B] = 15 uM, [C] = 3 uM, and [D] = 5 uM. R = 8.314 J/mol⋅K. Give your answer to the nearest hundredths in J/mol, but only provide the numerical value (i.e. don't include units in your answer).

Respuesta :

Answer:

The value of ΔG° of the reaction is 5704.82 J/mol.

Explanation:

A + B ⇄ C + D

Equilibrium concentrations of reactants an products:

[A] = 10 μM, [B] = 15 μM, [C] = 3 μM, and [D] = 5 μM

An equilibrium constant of the reaction can be written as:

[tex]K=\frac{[C][D]}{[A][B]}[/tex]

[tex]K=\frac{3 \mu M\times 5 \mu M}{10 \mu M\times 15 \mu M}=0.1[/tex]

[tex]\Delta G^o=-RT\ln K_1[/tex]

where,

R = Gas constant = [tex]8.314J/K mol[/tex]

T = temperature = [tex]25^oC=[273+25]K=298K[/tex]

[tex]K_1[/tex] = equilibrium constant at 25°C =  0.1

Putting values in above equation, we get:

[tex]\Delta G^o=-(8.314J/Kmol)\times 298K\times \ln (0.1)[/tex]

[tex]\Delta G^o=5704.82 J/mol[/tex]

The value of ΔG° of the reaction is 5704.82 J/mol.