Calculate the values of K, ΔG° (in kJ), and ΔS° (in J/K). Given 2.56 atm of A2(g) and 2.56 atm of B2(g) were mixed in a 1.00 L cylinder at 25°C and allowed to reach equilibrium.

Question

Consider the reaction

A₂(g) + B₂(g)  2 C(g) where ΔH° = −104.3 kJ.

In a particular experiment, 2.56 atm of A₂(g) and 2.56 atm of B₂(g) were mixed in a 1.00 L cylinder at 25°C and allowed to reach equilibrium. Then the molecules of A₂(g) were counted by using a very sensitive technique, and 2.82 ✕ 10¹³ molecules were found. For this reaction, calculate the values of K, ΔG° (in kJ), and ΔS° (in J/K).

Answer 1

Using the initial partial pressure of A₂ and the ideal gas law, you can find the initial moles of A₂

PV = nRT

n = (2.56 atm)(1 L)/(0.08206)(298 K) = 0.105 mol A₂ = 0.105 mol B₂

Using Avogadro's number, you can find the moles of A₂ at equilibrium. The moles of A₂ and B₂ are the same since they started at the same partial pressure and are used in equimolar amounts.

(2.82e13 molecules) * (1 mol/6.02e23 molecules) = 4.68e-11 moles A₂ = moles B₂

Based on the reaction, 2 moles of C are formed for each mole of A₂ used.

0.105 mol A₂ initial - (4.68e-11 mol A₂ at equilibrium) = 0.104999 mol A₂ used

0.104999*2 = 0.209998 mol C at equilibrium

To find the equilibrium constant, K, use the following equation, based on the reaction coefficients. These are the concentrations of the components (moles/L), and all the volumes are 1.0 L, so these can be ignored.

K = [C]²/([A₂][B₂]) = (.209998)²/((4.68e-11)(4.68e-11)) = 2.013e19

The Gibbs free energy (ΔG) can be calculated from the following equation:

ΔG = - RTlnK = - 8.314 J/mol/K * 298K * ln(2.013e19) * 0.209998 mol C = -23,126 J = -23.1 kJ in terms of C produced

To find the entropy (ΔS), use the following equation:

ΔG = ΔH - T*ΔS

ΔS = (ΔG - ΔH)/(-T) = (-23.1 kJ - (-104.3 kJ))/(-298 K) = -0.27 kJ/K = -272 J/K

Note: It seems odd that ΔH is given in kJ and not kJ/mol for the reaction. You may need to multiply ΔH by 0.20998 mol in the above equation, giving an answer of ΔS = 4 J/K.