Question

If O₂ gas is bubbled through water at 303 K, the number of millimoles of O₂ gas that dissolve in 1 litre of water is_______. (Nearest integer)
(Given : Henry’s Law constant for O₂ at 303 K is 46.82 k bar and partial pressure of O₂ = 0.920 bar)
(Assume solubility of O₂ in water is too small, nearly negligible)

Answer 1

Correct Answer: 1

To find the number of millimoles of O₂ that dissolve in 1 litre of water, we employ Henry's Law. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Mathematically, it is expressed as:
P = kH × x 
where:

• P is the partial pressure of the gas (0.920 bar).
• kH is the Henry's Law constant (46.82 k bar = 46820 bar, since 1 k bar = 1000 bar).
• x is the mole fraction of the gas in solution.

We rearrange the formula to solve for x:
x = P / kH = 0.920 / 46820

Calculating x gives us:
x ≈ 1.965 × 10^-5

For ideal dilute solutions, the molality is approximately equal to the mole fraction when the solubility is negligible. Thus, we can find the number of moles of O₂ by multiplying x by the number of moles of water in 1 litre. The molar mass of water is approximately 18 g/mol, and 1 litre of water is about 1000 g, equivalent to (1000 g) / (18 g/mol) ≈ 55.56 moles.
Therefore, the number of moles of O₂ is approximately:
moles of O₂ = x × 55.56 ≈ 1.092 × 10^-3

To convert to millimoles, multiply by 1000:
millimoles = 1.092 × 10^-3 × 1000 = 1.092

Rounding to the nearest integer, we find that the number of millimoles of O₂ is:
1

Answer 2

According to Henry’s law,
\(X(\text{oxygen}) = \frac{p(\text{oxygen})}{K_H} = \frac{0.920}{46.82 \times 10^3} = 1.96 \times 10^{-5}\)

Since, 1 litre of water contains 55.5 mol of it,
therefore,\(→ n \) represents moles of O₂ in solution.
\(X(\text{oxygen}) = \frac{n}{n + 55.5} \approx \frac{n}{55.5}\)

\(\frac{n}{55.5} = 1.96 \times 10^{-5}\)

\(n = 108.8 \times 10^{-5} = 1.08 \times 10^{-3} \, \text{moles}\)
m moles of oxygen = 1.08 × 10^–3 × 10³= 1 m mole
So, the answer is 1.