Mount Everest (a) Determine the number of molecules per unit...

Mount Everest (a) Determine the number of molecules per unit volume in the atmosphere at the top of Mount Everest. The pressure is $0.31 \times 10^{5} \mathrm{N} / \mathrm{m}^{2},$ and the temperature is $-30^{\circ} \mathrm{C}$ (b) Determine the number of molecules per unit volume at sea level, where the pressure is $1.0 \times 10^{5} \mathrm{N} / \mathrm{m}^{2}$ and the temperature is $20^{\circ} \mathrm{C}$

Key Concepts

Pressure

Pressure is a measure of the force exerted per unit area by gas molecules impinging on surfaces. It is a key variable in the Ideal Gas Law and directly influences the behavior and properties of gases, including the determination of the number density, which is a pivotal concept in studying various atmospheric conditions.

Temperature Conversion

Temperature conversion, especially from Celsius to Kelvin, is critical when applying the Ideal Gas Law because the equation requires temperatures in the absolute scale. This conversion ensures that calculations of molecular energy and density are accurate and consistent with the fundamental principles of thermodynamics.

Ideal Gas Law

The Ideal Gas Law relates the macroscopic properties of gases, namely pressure, volume, and temperature, to the number of molecules or moles present. It is expressed as PV = nRT for moles or p = nkT for individual molecules, where k is the Boltzmann constant. This law is fundamental in determining the number density of gas molecules under given conditions.

Number Density

Number density is the measurement of the number of particles per unit volume in a substance. In the context of the Ideal Gas Law, it is derived by rearranging the equation to solve for n/V, resulting in a direct relationship between pressure, temperature, and the concentration of molecules. This concept is essential for understanding the distribution of molecules in different atmospheric layers.

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