Question 29 of 36intermediate🔧 ApplyNumerical3 marks

Calculate the molarity of a solution of ethanol in water, in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).

Correct Answer

2.31 M

Exercise: EXERCISES | Q: 1.29 | (Page 27)
For More Understanding

Explanation

To find the molarity, we first use the given mole fraction of ethanol (0.040) to determine the moles of water. Assuming the total number of moles in the solution is 1, the moles of water will be 0.960. Using the molar mass of water (18.02 g) from the context and the given density of water (1 g/mL), we calculate the volume of the solvent (water) in litres. Since the solution is dilute, the volume of the solution is approximately equal to the volume of the water. Finally, we divide the moles of ethanol by the volume of the solution in litres to get the molarity.

Solution Steps

  1. Step 1: Determine moles of ethanol and water Given, mole fraction of ethanol = 0.040 Mole fraction of water = 1−0.040=0.9601 - 0.040 = 0.960 Assume total moles of solution = 1 mol Moles of ethanol = 0.040 mol Moles of water = 0.960 mol

  2. Step 2: Calculate the volume of water in litres Molar mass of water = 18.02 g Mass of water = 0.960 mol×18.02 g/mol=17.2992 g0.960 \text{ mol} \times 18.02 \text{ g/mol} = 17.2992 \text{ g} Since density of water = 1 g/mL, Volume of water = 17.2992 mL=0.0172992 L17.2992 \text{ mL} = 0.0172992 \text{ L} For a dilute solution, volume of solution ≈\approx volume of water = 0.0172992 L

  3. Step 3: Calculate the molarity of the solution

    Molarity (M)=No. of moles of soluteVolume of solution in litres\text{Molarity (M)} = \frac{\text{No. of moles of solute}}{\text{Volume of solution in litres}} Molarity (M)=0.040 mol0.0172992 L=2.312 M\text{Molarity (M)} = \frac{0.040 \text{ mol}}{0.0172992 \text{ L}} = 2.312 \text{ M}

    Thus, the molarity of the ethanol solution is approximately 2.31 M.

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