If the temperature and amount of a gas are held constant,...

If the temperature and amount of a gas are held constant, the pressure (P) it exerts is inversely proportional to volume (V). This means that pressure is directly proportional to the inverse of volume, or $1 /$ V. Write this as a proportionality, and then as an equation with $\mathrm{k}^{\prime}$ as the proportionality constant. What are the units of $\mathbf{k}^{\prime}$ if pressure is in atmospheres and volume is in liters?

Key Concepts

Unit Analysis

Unit analysis, or dimensional analysis, is the technique used to determine the units of a derived quantity by combining the units of the quantities involved in an equation. In this problem, unit analysis is employed to find the units of the proportionality constant k' by considering the units of pressure (atmospheres) and volume (liters), leading to the conclusion that k' has units of atmospheres·liters.

Boyle's Law

Boyle's Law is a fundamental principle in gas behavior stating that the pressure of a fixed amount of gas is inversely proportional to its volume when the temperature remains constant. This relationship is typically expressed as P ? 1/V or PV = constant, and it is a key concept in understanding the behavior of ideal gases.

Inverse Proportionality

Inverse proportionality is a relationship between two quantities where an increase in one results in a proportional decrease in the other, and vice versa. This means that one quantity, when multiplied by the other, remains constant. In the context of gas pressure and volume, when one increases, the other decreases such that their product is constant.

Proportionality Constant

The proportionality constant is a fixed value that relates two quantities in a proportionality equation. It quantifies the direct or inverse relationship between the variables. In this problem, the constant k' provides the specific scaling factor in the equation that equates the product of pressure and volume to a constant value.

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