CO₂ gas is bubbled through water during a soft drink manufacturing process at 298 K. If CO₂ exerts a partial pressure of 0.835 bar then x m mol of CO₂ would dissolve in 0.9 L of water. The value of x is ____________. (Nearest integer)
(Henry's law constant for CO₂ at 298 K is 1.67 × 10³ bar)

Solution

Chemistry ma’am · 4 steps

Henry's law gives the mole fraction of CO2. Multiply it by the moles of water, and you are nearly done.

1. Mole fraction. Henry's law is p = K_H x. Here K_H is in bar, so it links pressure straight to the mole fraction of the dissolved gas.

   x_(CO₂) = p/K_H = 0.835/(1.67 × 10³) = 5 × 10⁻⁴

2. Moles of water. 0.9 L of water has a mass of 900 g, so n_(H₂O) = 900/18 = 50 mol.
3. Moles of CO2. The mole fraction is tiny, so n_(CO₂) ≪ n_(H₂O) and x_(CO₂) ≈ n_(CO₂)/n_(H₂O). That gives n_(CO₂) = 5 × 10⁻⁴ × 50 = 0.025 mol.
4. So. 0.025 mol = 25 mmol, so x is 25.

The common slip: 28. Using 55.5 mol of water, which is the value for 1 L, gives about 28, not 25. Here only 0.9 L, or 50 mol, of water is present.

The idea to keep. When K_H is given in bar, p/K_H is the mole fraction. Turn that into moles using the moles of solvent, and drop the gas's moles from the denominator because the gas dissolves so sparingly.

Answer from the NTA final answer key. Solution by PrepWiser.