GATE 2020 CY – Question 63
At 30°C, 1.0 M aqueous sucrose has vapour pressure 31.207 mmHg and density 1.1256 g/mL. Pure-water vapour pressure is 31.824 mmHg. Sucrose molar mass is 342.3 g/mol. Find water activity coefficient to 3 decimals.
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Correct answer: 1.002 to 1.004
Explanation
Take 1 L solution: total mass 1125.6 g and sucrose mass 342.3 g, leaving 783.3 g water. Using Mw ≈ 18 g/mol gives nw = 43.5167 mol and $x_w=n_w/(n_w+1)=0.97754$. Water activity is $a_w=p/p^0=31.207/31.824=0.98061$. Thus $\gamma_w=a_w/x_w=1.003$, to three decimals. The molarity refers to a litre of solution, not a litre of pure solvent.
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