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What is the equation relating the volume of a gas π to the number of moles of the gas π and its molar volume π m?
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The relationship between the volume of a gas and the number of moles of the gas is described by Avogadroβs law, which states that the volume and number of moles of a gas are directly proportional at constant temperature and pressure.
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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.
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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.
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Shown here is the graph of a generic direct proportion, where π¦ is directly proportional to π₯.
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The equation for the trend line of a direct proportion has the same general formula as a linear equation, π¦ equals π times π₯ or π¦ equals π₯ times π, where π is a proportionality constant, a value used to relate π₯ and π¦.
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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.
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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 π m.
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The molar volume indicates the volume occupied by one mole of a gas at a specific temperature and pressure.
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This value will change as the temperature or pressure are changed.
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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.
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So, the equation which relates the volume of a gas, the number of moles of the gas, and its molar volume is π equals ππ m.