Question

What is the concentration of sugar (C₁₂H₂₂O₁₁) in mol L^–1 if its 20 g are dissolved in enough water to make a final volume up to 2L?

Answer 1

Given Data

Solute: sugar (sucrose), \( \text{C}_{12}\text{H}_{22}\text{O}_{11} \) 
Mass of sugar \( = 20 \, \text{g} \) 
Final volume of solution \( = 2.0 \, \text{L} \)

Step 1: Molar Mass of Sucrose

\[ M(\text{C}_{12}\text{H}_{22}\text{O}_{11}) = 12 \times 12 + 22 \times 1 + 11 \times 16 = 144 + 22 + 176 = 342 \, \text{g mol}^{-1} \]

Step 2: Moles of Sugar

\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{20}{342} \approx 0.0585 \, \text{mol} \]

Step 3: Molarity of the Solution

Molarity \( M = \dfrac{n}{V} \) (with \(V\) in litres).
\[ M = \frac{0.0585}{2.0} = 0.02925 \, \text{mol L}^{-1} \]

Concentration of sugar \( \approx 2.93 \times 10^{-2} \, \text{mol L}^{-1} \).