Ideal Gas Law The pressure P of a sample of gas is directly...

Ideal Gas Law The pressure $P$ of a sample of gas is directly proportional to the temperature $T$ and inversely proportional to the volume $V$. (a) Write an equation that expresses this variation. (b ) Find the constant of proportionality if $100 \mathrm{L}$ of gas exerts a pressure of $33.2 \mathrm{kPa}$ at a temperature of $400 \mathrm{K}$ (absolute temperature measured on the Kelvin scale). (c) If the temperature is increased to $500 \mathrm{K}$ and the volume is decreased to $80 \mathrm{L}$, what is the pressure of the gas?

Ideal Gas Law The pressure $P$ of a sample of gas is directly proportional to the temperature $T$ and inversely proportional to the volume $V$.
(a) Write an equation that expresses this variation.
(b ) Find the constant of proportionality if $100 \mathrm{L}$ of gas exerts a pressure of $33.2 \mathrm{kPa}$ at a temperature of $400 \mathrm{K}$ (absolute temperature measured on the Kelvin scale).
(c) If the temperature is increased to $500 \mathrm{K}$ and the volume is decreased to $80 \mathrm{L}$, what is the pressure of the gas?

Key Concepts

Direct Proportionality

Direct proportionality refers to a relationship between two variables in which they increase or decrease together in a constant ratio. In the context of gases, this means that if the temperature increases (and volume remains constant), the pressure will also increase proportionally.

Inverse Proportionality

Inverse proportionality describes a relationship where one variable increases while the other decreases so that their product remains constant. For gases, this implies that if the volume decreases (with temperature held constant), the pressure increases, since pressure is inversely proportional to volume.

Constant of Proportionality

The constant of proportionality is a fixed value that links the related variables in a proportional relationship. In the equation expressing the gas law, it serves as the multiplier that converts the ratio of temperature to volume into the corresponding pressure, and its value is determined using specific conditions provided.

Formulating and Applying Variation Equations

This involves setting up an equation that shows how a variable depends directly on one quantity and inversely on another (for example, P = k*(T/V)). Once the constant k is determined using known conditions, the equation can be used to predict outcomes under different scenarios, a process that is essential in solving problems in gas behavior and other similar physical relationships.

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