Question

When baking soda is heated it decomposes according to the following reaction:

2NaHCO3(s) <------ -------> Na2 CO3(s) +H2O(g)+CO2(g)

If sufficient baking soda is placed in an evacuated container and heated to 90 ºC, the total pressure of the gases is 0.5451 atm.

What is the value of Kp at that temperature?

Answer 1

The decomposition reaction is given.

2 NaHCO₃ (s) <======> Na₂CO₃ (s) + H₂O (g) + CO₂ (g)

Since we have gaseous products and no gaseous reactants, we can write the equilibrium constant expression as

K_p = (P_H2O).(P_CO2) where the P terms denoted equilibrium partial pressures of the gases at 90⁰C.

Also, P_tot = P_H2O + P_CO2 where P_tot is the total pressure of the system.

As per the balanced stoichiometric equation,

2 moles NaHCO₃ = 1 mole H₂O = 1 mole CO₂

Total number of moles of gaseous products = 1+1 = 2

Mole fraction of H₂O, X_H2O = (1 mole)/(2 mole) = 0.5 mole

Mole fraction of CO₂, X_CO2 = (1 mole)/(2 mole) = 0.5 mole.

P_H2O = X_H2O*P_tot = (0.5)*(0.5451 atm) = 0.27255 atm.

P_CO2 = X_CO2*P_tot = (0.5)*(0.5451 atm) = 0.27255 atm.

Therefore, K_p = (0.27255)*(0.27255) = 0.07428 ≈ 0.074 (ans) (we neglect the unit since this is an equilirium constant).