At the top of a mountain, a thermometer reads 7 " C and a barometer reads 70 cm of mercury. At

step 1 So let's solve this question. So we have P1 v1 x1 equals to P2 b2 by T2 or P1 M v1 m by D1 equal

At the top of a mountain, a thermometer reads 7 " C and a...

At the top of a mountain, a thermometer reads $7 " \mathrm{C}$ and a barometer reads $70 \mathrm{~cm}$ of mercury. At the botom of the mountain, they read $27^{\circ} \mathrm{C}$ and $76 \mathrm{~cm}$ of mercury, respectively. Compare the density of air at the top with that at the botom.

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental principle that relates the pressure, volume, temperature, and amount of a gas. When considering the density of a gas, this law helps establish that density is proportional to pressure and inversely proportional to temperature, assuming a fixed molar mass. This relationship is crucial in comparing gas densities under different environmental conditions.

Air Density Dependence on Pressure and Temperature

Air density is determined by the ratio of pressure to temperature, as derived from the ideal gas law. When pressure increases or temperature decreases, the density of air increases, and vice versa. This concept is key in understanding how atmospheric conditions vary with altitude.

Barometric Pressure Measurement

Barometers measure atmospheric pressure, which is a key factor in determining air density. Understanding how barometric readings change with altitude is essential, as it provides the necessary data to compare the density of air at different elevations.

Temperature Effects on Gas Behavior

Temperature affects the kinetic energy of gas molecules, influencing their velocity and the space they occupy. A higher temperature generally means increased molecular motion and expanded volume, leading to lower density if the pressure remains constant. This concept is important when comparing the density of air at different temperatures.

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