Question Video: Recalling the Equation That Relates Volume, Moles, and Molar Gas Volume Chemistry

What is the equation relating the volume of a gas, 𝑉, to the number of moles of the gas, 𝑛, and its molar volume, 𝑉_m?

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Video Transcript

What is the equation relating the volume of a gas 𝑉 to the number of moles of the gas 𝑛 and its molar volume 𝑉 m?

The relationship between the volume of a gas and the number of moles of the gas is described by Avogadro’s law, which states that the volume and number of moles of a gas are directly proportional at constant temperature and pressure. This means that as the number of moles of a gas are increased, the volume occupied by that gas will also increase at a constant rate. Because these two quantities are directly proportional at constant temperature and pressure, a graph of the number of moles of a gas versus its volume will exactly fit a linear trend line, which passes through the origin.

Shown here is the graph of a generic direct proportion, where 𝑦 is directly proportional to π‘₯. The equation for the trend line of a direct proportion has the same general formula as a linear equation, 𝑦 equals π‘˜ times π‘₯ or 𝑦 equals π‘₯ times π‘˜, where π‘˜ is a proportionality constant, a value used to relate π‘₯ and 𝑦. As volume and the number of moles of a gas are directly proportional, we can surmise that the equation for the trend line must be volume equals the number of moles times a proportionality constant π‘˜.

The proportionality constant used to relate the volume and the number of moles of a gas is called the molar volume and is given the symbol 𝑉 m. The molar volume indicates the volume occupied by one mole of a gas at a specific temperature and pressure. This value will change as the temperature or pressure are changed. If we substitute the molar volume for π‘˜ in the equation, we get the equation volume equals the number of moles times the molar volume. So, the equation which relates the volume of a gas, the number of moles of the gas, and its molar volume is 𝑉 equals 𝑛𝑉 m.

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