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 𝑥. The equation for the trend line of
a direct proportion has the same general formula as a linear equation, 𝑦 equals 𝑘
times 𝑥 or 𝑦 equals 𝑥 times 𝑘, where 𝑘 is a proportionality constant, a value
used to relate 𝑥 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
𝑘.
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 𝑘 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.
