The reversible reaction: goes completely to the right at temperature above and remains completely on — Thermodynamics and Thermochemistry Chemistry Question
Question
The reversible reaction: $\text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O} \to \text{Na}_2\text{SO}_4 + 10\text{H}_2\text{O}; \Delta H = +16.1\text{ kcal}$ goes completely to the right at temperature above $32.4^\circ\text{C}$ and remains completely on the left below this temperature. This system has been used in some solar houses for heating at night with the energy absorbed from the sun’s radiation during the day. How many litres of fuel gas could be saved per night by the reversal of the dehydration of a fixed charge of 100 kg $\text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O}$? Assume that the fuel value of the gas is $10,000\text{ kcal/m}^3$.
💡 Solution & Explanation
Molar mass of Glauber's salt ($\text{Na}_2\text{SO}_4 \cdot 10\text{H}_2\text{O}$) = $322\text{ g/mol}$. Moles in 100 kg = $100000 / 322 = 310.56\text{ mol}$. Energy stored = $310.56 \times 16.1 = 5000\text{ kcal}$. Volume of fuel gas equivalent = $5000\text{ kcal} / 10000\text{ kcal/m}^3 = 0.5\text{ m}^3$. In litres, $0.5 \times 1000 = 500\text{ L}$. Format as 0500.