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Hydrogen gas is collected over water at 24°C. The total pressure of the sample is 100.6 kPa. At 24°C, the vapor pressure of water is 22.0 mmHg. What is the partial pressure of the hydrogen gas?

(Answer: 733 mmHg or 97.7 kPa)

Answer :

The partial pressure of the hydrogen gas collected over water at 24°C is approximately 97,700 Pa.

We move ahead to solve this question by using the principles of partial pressures in Physical chemistry, with the main one being Dalton's Law of partial pressures.

Partial pressure is defined as the pressure which a component of a mixture of volume V would exert if it individually occupied the same total volume.

Dalton's Law provides an excellent relation to calculate the partial pressures of any component of a mixture.

  • The total pressure offered by a mixture is the sum of the partial pressures of all its components.
  • Partial Pressure of a component = Mole Fraction of the component * Total pressure of the mixture

In this question, the partial pressure of Hydrogen gas in water is equal to the difference between the Total pressure and the pressure of plain water at that temperature, by applying Dalton's Law.

Vapor pressure of Water at 24°C = 22.0 mmHg

We need them in different units, so we convert them.

1 mmHg ≈ 133.32Pa

Thus,

Vapor Pressure = 22 * 133.32

= 2933.04 Pa = 2.933 kPa

We already have the total pressure given as 100.6kPa.

Therefore, the partial pressure of H₂ gas is

P.P = Total pressure - Vapor Pressure

P.P = 100.6 - 2.933

Partial Pressure = 97.66kPa ≈ 97700 Pa

So, the partial pressure of H₂ gas, in this case, is 97700 Pa.

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