Calculate the mass of ascorbic acid (Molar mass = 176 g mol–1) to be dissolved in 75 g ofacetic acid, to lower its freezing point by 1·5°C.(Kf = 3·9 K kg mol–1)
Question
Calculate the mass of ascorbic acid (Molar mass = 176 g mol–1) to be dissolved in 75 g ofacetic acid, to lower its freezing point by 1·5°C.(Kf = 3·9 K kg mol–1)
Solution
Sure, let's solve this step by step.
Step 1: We know that the depression in freezing point (ΔTf) is given by the formula ΔTf = Kf * m, where Kf is the cryoscopic constant and m is the molality.
Step 2: We can rearrange this formula to find the molality: m = ΔTf / Kf. Substituting the given values, we get m = 1.5°C / 3.9 K kg mol–1 = 0.3846 mol/kg.
Step 3: Molality is also defined as the number of moles of solute per kilogram of solvent. So, we can say that 0.3846 mol of ascorbic acid is present in 1 kg of acetic acid.
Step 4: We need to find the mass of ascorbic acid in 75 g of acetic acid. First, convert 75 g to kg, which gives 0.075 kg.
Step 5: Now, multiply the molality by the mass of the solvent to find the number of moles of ascorbic acid: 0.3846 mol/kg * 0.075 kg = 0.028845 mol.
Step 6: Finally, multiply the number of moles by the molar mass to find the mass of ascorbic acid: 0.028845 mol * 176 g/mol = 5.08 g.
So, you need to dissolve approximately 5.08 g of ascorbic acid in 75 g of acetic acid to lower its freezing point by 1.5°C.
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