A crystalline hydrated salt of sodium sulphate () on being heated strongly loses exactly of its init — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
A crystalline hydrated salt of sodium sulphate ($Na_2SO_4 \cdot xH_2O$) on being heated strongly loses exactly $55.9\%$ of its initial mass to become completely anhydrous. Find the exact integer value of the water of crystallization ($x$). (Atomic weights: Na=23, S=32, O=16, H=1).
💡 Solution & Explanation
Step 1: Calculate the molar mass of anhydrous $Na_2SO_4 = (23 \times 2) + 32 + (16 \times 4) = 142\text{ g/mol}$. Step 2: The total molar mass of the hydrate is $142 + 18x$. Step 3: The mass lost upon heating is the mass of the water, which is $18x$. Set up the percentage loss equation: $\frac{18x}{142 + 18x} = 0.559$. Step 4: Solve for $x$. $18x = 0.559 \times (142 + 18x) \implies 18x = 79.378 + 10.062x \implies 7.938x = 79.378 \implies x \approx 10$. The salt is Glauber's salt, $Na_2SO_4 \cdot 10H_2O$.