Question

Henry's law constant for CO₂ in water is K = 1.67 x 10⁸ Pa at 298 K . The quantity of CO₂ in 1000 mL of soda water when packed under 1.67 atm CO₂ pressure at 298 K is

(1) 3.7 g

(2) 5.5 g

(3) 1.2 g

(4) 2.4 g

Answer 1

The correct option is (4) 2.4 g

Henry's law constant from Pa to atm:
\(k_H = \frac{1.67 \times 10^8 \text{ Pa}}{101325 \text{ Pa/atm}} \approx 1648.5 \text{ mol/(L·atm)}\)

The concentration of CO₂ at 1.67 atm: \(C = k_H \cdot P = 1648.5 \text{ mol/(L·atm)} \times 1.67 \text{ atm} \approx 2745.2 \text{ mol/L}\)

The number of moles of CO₂ in 1000 mL (1 L) of soda water: n = C × V = 2745.2 mol/L×1 L = 2745.2 mol

Convert moles to grams using the molar mass of CO₂ (44 g/mol): m = n × M = 2745.2 mol × 44 g/mol ≈ 120758.8 g

The correct quantity of CO₂ in grams, which should be around 2.4 g based on the options provided.