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Ch.13 - Solutions & Their Properties
Chapter 13, Problem 83

Hydrogen sulfide, H₂S, is a toxic gas responsible for the odor of rotten eggs. The solubility of H₂S in water at STP is 0.195 M. What is the Henry’s law constant of H₂S at 0 °C? What is the solubility of H₂S in water at 0 °C and a partial pressure of 25.5 mm Hg?

Verified step by step guidance
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Step 1: Understand Henry's Law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. The formula is given by S = k_H * P, where S is the solubility, k_H is the Henry's law constant, and P is the partial pressure of the gas.
Step 2: To find the Henry's law constant (k_H) for H₂S at 0 °C, use the given solubility at STP (0.195 M) and the standard pressure at STP (1 atm or 760 mm Hg). Rearrange the formula to solve for k_H: k_H = S / P.
Step 3: Convert the pressure from mm Hg to atm if necessary, using the conversion factor 1 atm = 760 mm Hg. This will ensure consistency in units when calculating k_H.
Step 4: Calculate the solubility of H₂S at 0 °C and a partial pressure of 25.5 mm Hg using the Henry's law constant found in Step 2. Use the formula S = k_H * P, substituting the new pressure value.
Step 5: Convert the pressure of 25.5 mm Hg to atm if needed, and use this value in the formula to find the new solubility of H₂S in water at the given conditions.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Henry's Law

Henry's Law states that the amount of gas that dissolves in a liquid at a given temperature is directly proportional to the partial pressure of that gas above the liquid. This relationship can be expressed mathematically as C = kH * P, where C is the concentration of the gas in the liquid, kH is the Henry's law constant, and P is the partial pressure of the gas.
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Solubility

Solubility refers to the maximum amount of a substance that can dissolve in a solvent at a specific temperature and pressure. For gases, solubility is influenced by factors such as temperature and pressure, with higher pressures generally increasing solubility. In the case of H₂S, its solubility in water can change with temperature and the partial pressure of the gas.
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Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a reference point used in chemistry, defined as 0 °C (273.15 K) and 1 atm pressure. At STP, the behavior of gases can be predicted using the ideal gas law, and it serves as a baseline for comparing the solubility and other properties of gases in different conditions. Understanding STP is crucial for calculating changes in solubility and gas behavior.
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