Sodium carbonate can be made by heating sodium bicarbonate:
2NaHCO3(s) �¨ Na2CO3(s) + CO2(g) + H2O(g)
Given that ƒ¢H�‹ = 128.9 kJ/mol and ƒ¢G�‹ = 33.1 kJ/mol at 25�‹C, above what minimum temperature will the reaction become spontaneous under standard state conditions? Report the temperature in �‹C.
government's
To determine the minimum temperature at which the reaction becomes spontaneous under standard state conditions, we need to calculate the change in free energy (∆G) using the equation:
∆G = ∆H - T∆S
where ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy.
Given that ∆H = 128.9 kJ/mol and ∆G = 33.1 kJ/mol, we can rearrange the equation to solve for T:
∆G = ∆H - T∆S
33.1 kJ/mol = 128.9 kJ/mol - T∆S
Since the reaction produces one molecule of CO2 and one molecule of H2O, the change in entropy (∆S) can be calculated using the formula:
∆S = ∆S_CO2 + ∆S_H2O
The entropy change for CO2 (∆S_CO2) and H2O (∆S_H2O) can be found in reference books or online databases.
Now, we can substitute the values into the equation and solve for T:
33.1 kJ/mol = 128.9 kJ/mol - T(∆S_CO2 + ∆S_H2O)
Solving for T will give us the minimum temperature required for the reaction to become spontaneous under standard state conditions.