Question

A flask containing a mixture of A and B at equilibrium was discovered, and the concentration of A at room temperature was determined experimentally to be 3.1*10^-2 mol/L. What is the concentration of B? Background info, Consider a hypothetical equilibrium that exists between compounds A and B at room temperature (298K). The delta G for the forward reaction is 22 Kj/mol. Likewise, delta G for the reverse process has been determined to be 34 Kj/mol. First calculate delta G for the forward reaction. I NEED HELP WITH THE FIRST PART TO FIND CONCENTRATION OF B?

Answer 1

A      B

G = 22 kJ/mol - 34 kJ/mol

= -12 kJ/mol

= -12000 J/mol

R = 8.314 J/(mol K)

T = 298 K

Now,

G = - RT ln K

where K is the equilibrium constant,

But, K = [B] / [A]

= [B] / (3.1 x 10^-2 mol/L)

So,

G = - RT ln K   

- 12000 J/mol = - 8.314 J/(mol K) * 298 K * ln ( [B] / (3.1 x 10^-2 mol/L) )

- 12000 = - 8.314 * 298 * ln ( [B] / (3.1 x 10^-2 mol/L) )

ln ( [B] / (3.1 x 10^-2 mol/L) ) = - 12000 / ( - 8.314 * 298)

ln ( [B] / (3.1 x 10^-2 mol/L) ) = 4.84

[B] / (3.1 x 10^-2 mol/L) = e^4.84

[B] / (3.1 x 10^-2 mol/L) = 126.47

[B] = 3.92 mol/L