Henry's Law
Henry's law constant for CO₂ dissolved in water at 298 K is 1.67 × 10⁸ Pa. What is the mole fraction of CO₂ in water when the partial pressure of CO₂ above the solution is 2.5 × 10⁵ Pa?
Select the correct option:
Solution
1.5 × 10⁻³
Henry's law states that the mole fraction of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the solution at constant temperature. Mathematically, p = K_H × x, where K_H is Henry's law constant and x is the mole fraction of the dissolved gas. Given: p = 2.5 × 10⁵ Pa, K_H = 1.67 × 10⁸ Pa. Therefore, x(CO₂) = p / K_H = (2.5 × 10⁵) / (1.67 × 10⁸) = 1.497 × 10⁻³ ≈ 1.5 × 10⁻³. Option 1.5 × 10⁻⁴ results from a factor of 10 arithmetic error, perhaps miscounting powers of 10. Option 3.4 × 10⁻³ comes from incorrectly inverting K_H incorrectly or using the wrong value. Option 6.7 × 10⁻³ results from using K_H = 3.73 × 10⁷ Pa instead of the given value. This directly applies the Henry's law equation from NCERT Chemistry Part I, Chapter 2 (Solutions). Henry's law is particularly important for understanding carbonated beverages and deep-sea diving physiology. Plausibility check: a small mole fraction (10⁻³ range) is expected since CO₂ is sparingly soluble in water under moderate pressures.
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About This Question
- Subject
- chemistry
- Chapter
- solutions
- Topic
- henry's law
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
1.5 × 10⁻³
Henry's law states that the mole fraction of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the solution at constant temperature. Mathematically, p = K_H × x, where K_H is Henry's law constant and x is the mole fraction of the dissolved gas. Given: p = 2.5 × 10⁵ Pa, K_H = 1.67 × 10⁸ Pa. Therefore, x(CO₂) = p / K_H = (2.5 × 10⁵) / (1.67 × 10⁸) = 1.497 × 10⁻³ ≈ 1.5 × 10⁻³. Option 1.5 × 10⁻⁴ results from a factor of 10 arithmetic error, perhaps miscounting powers of 10. Option 3.4 × 10⁻³ comes from incorrectly inverting K_H incorrectly or using the wrong value. Option 6.7 × 10⁻³ results from using K_H = 3.73 × 10⁷ Pa instead of the given value. This directly applies the Henry's law equation from NCERT Chemistry Part I, Chapter 2 (Solutions). Henry's law is particularly important for understanding carbonated beverages and deep-sea diving physiology. Plausibility check: a small mole fraction (10⁻³ range) is expected since CO₂ is sparingly soluble in water under moderate pressures.
This easy difficulty chemistry question is from the chapter solutions, covering the topic of henry's law. It appeared in the 2025 exam.
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