The partial pressure of O2 in air at sea level is 0.21 atm. Using the data in Table 13.1, together with Henry’s law, calculate the molar concentration of O2 in the surface water of a mountain lake saturated with air at 20 °C and an atmospheric pressure of 650 torr.

Verified step by step guidance

Step 1: Convert the atmospheric pressure from torr to atm. Use the conversion factor: 1 atm = 760 torr.

Step 2: Calculate the partial pressure of O2 at the mountain lake using the given atmospheric pressure and the fraction of O2 in air (0.21).

Step 3: Use Henry's Law to find the molar concentration of O2 in water. Henry's Law is given by: C = k_H * P, where C is the concentration, k_H is Henry's Law constant for O2 at 20 °C, and P is the partial pressure of O2.

Step 4: Look up the value of Henry's Law constant (k_H) for O2 at 20 °C from Table 13.1.

Step 5: Substitute the values of k_H and the partial pressure of O2 into the Henry's Law equation to calculate the molar concentration of O2 in the water.

Key Concepts

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

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture. In this context, it is the pressure of oxygen (O2) in the air, which is 0.21 atm at sea level. Understanding partial pressure is crucial for calculating the concentration of gases dissolved in liquids, as it directly influences the solubility of the gas according to Henry's law.

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 allows us to calculate the molar concentration of O2 in water by using the known partial pressure of O2 and the Henry's law constant for O2 at the specified temperature.

Atmospheric Pressure and Conversion

Atmospheric pressure is the pressure exerted by the weight of the atmosphere, typically measured in torr or atm. In this problem, the atmospheric pressure is given as 650 torr, which must be converted to atm for consistency with the partial pressure of O2. Understanding how to convert between these units is essential for accurate calculations in gas solubility and concentration.

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