Question

Solid NaHCO₃ is heated to 90°C. At equilibrium the total pressure of the gases produced is 0.545 atm. Calculate ΔG° at 90°C for the reaction 2 NaHCO₃(s) ⇌ Na₂CO₃(s) + H₂O(g) + CO₂(g).

Answer 1

Delta G° can be calculated from the total gas equilibrium pressure at 90°C using the relation to Kp and the equation ΔG° = -RT ln Kp, considering R = 8.314 J/mol·K and T = 363.15 K.

Step-by-step explanation:

To calculate ΔG° at 90°C for the decomposition of sodium hydrogen carbonate (NaHCO₃), we use the reaction 2 NaHCO₃(s) ⇌ Na₂CO₃(s) + H₂O(g) + CO₂(g). Since the pressure of gases at equilibrium is given as 0.545 atm, we can use the equation ΔG° = -RT ln Kp, where R is the gas constant (8.314 J/mol·K) and T is the temperature in kelvins (90°C = 363.15 K).

The equilibrium constant Kp is related to the total pressure of the gases produced assuming ideal behavior and equal moles of H₂O and CO₂ since they are in a 1:1 ratio from the stoichiometry of the reaction. Equal moles of H₂O and CO₂ imply that each has a partial pressure of 0.2725 atm (half the total pressure).

Kp is then the product of the partial pressures of the gaseous products over the reactants (since the reactants are solids, they don't appear in the expression for Kp). Thus, Kp equals (0.2725 atm)². Inserting these values into the equation will give us ΔG° at 90°C for the reaction.