The Henry's law constant for the solubility of oxygen in...

The Henry's law constant for the solubility of oxygen in water is $3.30 \times 10^{-4}$ M/atm at $12^{\circ} \mathrm{C}$ and $2.85 \times 10^{-4} \mathrm{M} / \mathrm{atm}$ at $22{ }^{\circ} \mathrm{C}$. Air is $21 \mathrm{~mol} \%$ oxygen. (a) How many grams of oxygen can be dissolved in one liter of a trout stream at $12^{\circ} \mathrm{C}\left(54^{\circ} \mathrm{F}\right)$ at an air pressure of $1.00 \mathrm{~atm} ?$ (b) How many grams of oxygen can be dissolved per liter in the same trout stream at $22^{\circ} \mathrm{C}\left(72^{\circ} \mathrm{F}\right)$ at the same pressure as in (a)? (c) A nuclear power plant is responsible for the stream's increase in temperature. What percentage of dissolved oxygen is lost by this increase in the stream's temperature?

The Henry's law constant for the solubility of oxygen in water is $3.30 \times 10^{-4}$ M/atm at $12^{\circ} \mathrm{C}$ and $2.85 \times 10^{-4} \mathrm{M} / \mathrm{atm}$ at $22{ }^{\circ} \mathrm{C}$. Air is $21 \mathrm{~mol} \%$ oxygen.
(a) How many grams of oxygen can be dissolved in one liter of a trout stream at $12^{\circ} \mathrm{C}\left(54^{\circ} \mathrm{F}\right)$ at an air pressure of $1.00 \mathrm{~atm} ?$
(b) How many grams of oxygen can be dissolved per liter in the same trout stream at $22^{\circ} \mathrm{C}\left(72^{\circ} \mathrm{F}\right)$ at the same pressure as in (a)?
(c) A nuclear power plant is responsible for the stream's increase in temperature. What percentage of dissolved oxygen is lost by this increase in the stream's temperature?

Key Concepts

Conversion of Molar Concentration to Mass

The conversion of molar concentration (moles per liter) to mass (grams per liter) involves multiplying the concentration by the molar mass of the gas. This step is often necessary to translate the amount of dissolved gas into a more practical and understandable measurement, like grams dissolved per liter.

Temperature Dependence of Gas Solubility

Temperature significantly affects the solubility of gases in liquids, generally causing gas solubility to decrease as temperature increases. This occurs because higher temperatures increase the kinetic energy of molecules, making it easier for gas molecules to escape from the liquid phase back into the gas phase. Understanding this concept is essential when comparing solubility under different temperature conditions.

Partial Pressure

Partial pressure refers to the pressure exerted by a single component of a gas mixture, such as oxygen in air. It is calculated by multiplying the total pressure of the mixture by the mole fraction of the gas of interest. This concept is crucial in applying Henry's Law because it determines the effective pressure driving the solvation of the gas in the liquid.

Henry's Law

Henry's Law describes the proportional relationship between the concentration of a dissolved gas in a liquid and the partial pressure of that gas above the liquid. It is typically expressed as C = k_H * P, where C is the concentration of the gas in the liquid, k_H is the Henry's law constant, and P is the partial pressure of the gas. This law is fundamental in understanding gas solubility in liquids under different pressures.

Gas Solubility

Gas solubility is a measure of how much gas can dissolve in a liquid at a given temperature and pressure. It depends on both the nature of the gas and the solvent, as well as environmental parameters such as temperature and pressure. Henry's Law provides a quantitative framework for understanding and calculating gas solubility in liquids.

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