Question 12 of 36intermediate🔧 ApplyNumerical3 marks

If the density of methanol is 0.793 kg L⁻¹, what is its volume needed for making 2.5 L of its 0.25 M solution?

Correct Answer

0.0252 L or 25.2 mL

Exercise: EXERCISES | Q: 1.12 | (Page 26)
For More Understanding

Explanation

To find the volume of methanol needed, we first calculate the required moles of methanol using the molarity and volume of the final solution. Then, we convert the moles to mass using the molar mass of methanol (32 g/mol). Finally, we use the given density to find the required volume.

Solution Steps

  1. Step 1: Calculate the number of moles of methanol required Using the formula for molarity, 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}} No. of moles = 0.25 mol L−1×2.5 L=0.625 mol0.25 \text{ mol L}^{-1} \times 2.5 \text{ L} = 0.625 \text{ mol}

  2. Step 2: Calculate the mass of methanol required The molar mass of methanol (CH3OH\text{CH}_3\text{OH}) is 32 g mol−132 \text{ g mol}^{-1}. Mass = No. of moles ×\times Molar mass = 0.625 mol×32 g mol−1=20 g=0.020 kg0.625 \text{ mol} \times 32 \text{ g mol}^{-1} = 20 \text{ g} = 0.020 \text{ kg}

  3. Step 3: Calculate the volume of methanol needed Using the density formula, Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}} Volume = MassDensity=0.020 kg0.793 kg L−1=0.02522 L\frac{\text{Mass}}{\text{Density}} = \frac{0.020 \text{ kg}}{0.793 \text{ kg L}^{-1}} = 0.02522 \text{ L} Therefore, the volume needed is 0.0252 L0.0252 \text{ L} or 25.2 mL25.2 \text{ mL}.

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