The vapor pressure of water at 40.0^∘ C is 7.34 ×10^3 N / m^2 . Using the ideal gas law, calcula

step 1 So here we're going to use the ideal gas law, the pressure times the volume equals the number of

The vapor pressure of water at 40.0^∘ C is 7.34 ×10^3 N /...

The vapor pressure of water at $40.0^{\circ} \mathrm{C}$ is $7.34 \times 10^{3} \mathrm{N} / \mathrm{m}^{2} .$ Using the ideal gas law, calculate the density of water vapor in $\mathrm{g} / \mathrm{m}^{3}$ that creates a partial pressure equal to this vapor pressure. The result should be the same as the saturation vapor density at that temperature $\left(51.1 \mathrm{g} / \mathrm{m}^{3}\right)$.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas (PV = nRT). It provides a framework to calculate various properties of gases, such as density, by incorporating the gas’s molar mass. This law is central to many problems in thermodynamics and is often used as a first approximation for real gases under moderate conditions.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a certain temperature. It reflects a substance's tendency to evaporate and is crucial for understanding phase changes, such as evaporation and condensation. In problems involving moist air, vapor pressure indicates the saturation point at which water vapor condenses into liquid water.

Density of Gases

Density of a gas is defined as its mass per unit volume. By combining the Ideal Gas Law with the gas’s molar mass, one can derive the density under specified conditions of pressure and temperature. This calculation is particularly useful in determining the concentration of gas-phase species in various applications, including atmospheric studies.

Partial Pressure

Partial pressure refers to the pressure that a single component of a gas mixture would exert if it alone occupied the entire volume. It is a fundamental concept in gas mixtures because it allows the evaluation of the contribution of individual gases to the total pressure, which is vital in systems where chemical equilibria involve gases.

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