Question

For the absorption of a gas (like carbon dioxide) into a liquid (like water) Henry's law states that partial pressure of the gas is proportional to the mole fraction of the gas in the liquid-gas solution with the constant of proportionality being Henry's constant. A bottle of soda pop \(\left(\mathrm{CO}_{2}-\mathrm{H}_{2} \mathrm{O}\right)\) at room temperature has a Henry's constant of \(17,100 \mathrm{kPa}\). If the pressure in this bottle is \(140 \mathrm{kPa}\) and the partial pressure of the water vapor in the gas volume at the top of the bottle is neglected, the concentration of the \(\mathrm{CO}_{2}\) in the liquid \(\mathrm{H}_{2} \mathrm{O}\) is (a) \(0.004 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (b) \(0.008 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (c) \(0.012 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (d) \(0.024 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\) (e) \(0.035 \mathrm{~mol}-\mathrm{CO}_{2} / \mathrm{mol}\)

Short answer

Answer: The concentration of CO2 in the liquid H2O is approximately 0.008 mol-CO2/mol.

Step-by-step solution

Recall the formula for Henry's law

According to Henry's law, the partial pressure of the gas (P) is proportional to the mole fraction (x) of the gas in the solution, with the constant of proportionality being Henry's constant (kH): P = kH * x Now, we will plug the given values into this equation to find the mole fraction of CO2 in the H2O.

Substitute the values and solve

Given: P = 140 kPa, kH = 17,100 kPa We need to find x: 140 = 17,100 * x Divide both sides by 17,100: x = 0.00818

Find the closest answer among the given options

Now, let's find the closest option to the calculated value: (a) 0.004 (b) 0.008 (c) 0.012 (d) 0.024 (e) 0.035 The closest option to 0.00818 is (b) 0.008. Therefore, the concentration of CO2 in the liquid H2O is approximately 0.008 mol-CO2/mol.