The relative humidity of air is calculated by the ratio of...

The relative humidity of air is calculated by the ratio of the partial pressure of water in the air to the equilibrium vapor pressure of water at the same temperature times $100 \%$. The average temperature and humidity of Sahara Desert are $40^{\circ} \mathrm{C}$ and $25 \%$ respectively. How many molecules of water are present in $1 \mathrm{~m}^{3}$ of air in Sahara Desert?

Key Concepts

Partial Pressure of Water Vapor

The partial pressure of water vapor is the contribution of water vapor to the total pressure of the air. It is determined by the amount of water vapor present and is used in conjunction with the equilibrium vapor pressure to calculate relative humidity. This concept is fundamental in understanding the behavior of water in gaseous mixtures.

Relative Humidity

Relative humidity is a measure of how much water vapor is present in the air relative to the maximum amount the air can hold at a given temperature. It is calculated by taking the ratio of the actual partial pressure of water vapor to the equilibrium (saturation) vapor pressure at that temperature, then multiplying by 100%. This concept is crucial in understanding atmospheric moisture and weather patterns.

Equilibrium Vapor Pressure

Equilibrium vapor pressure is the pressure exerted by a vapor when it is in thermodynamic equilibrium with its liquid phase at a given temperature. It represents the maximum pressure that water vapor can exert in the air without condensing, and serves as a baseline for assessing whether the air is saturated with moisture.

Ideal Gas Law

The ideal gas law, expressed as pV=nRT, relates the pressure, volume, temperature, and number of moles of a gas. In the context of atmospheric calculations, it is used to determine the number of moles or molecules of a gas in a given volume under specified conditions, providing a bridge between macroscopic measurements and molecular counts.

Avogadro's Number

Avogadro's number is a constant that defines the number of molecules or atoms in one mole of any substance. It is essential for converting the number of moles calculated via the ideal gas law into an actual count of molecules, thereby linking macroscopic chemical properties with microscopic details.

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