# 6.8: Gas Law Equations: Relating the Volume and Amount of a Gas

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Lorenzo Romano Amedeo Carlo Avogadro, an Italian scientist, studied how altering the quantity of a gas impacted its volume under isothermal and isobarometric conditions. Increasing the number of gaseous particles that are present in a flexible container causes the container to expand. Therefore, the volume and amount of a gas are *directly*, or *linearly*, proportional to one another, and dividing these quantities yields a constant, k_{4}. Like each of the previously-discussed constants, k_{4} is not a universal constant, because its value changes based on the identity of the gas that is being studied. Therefore, the most useful representation of **Avogadro's Law **directly relates the volume of an initial amount of a gas to the volume that corresponds to a final amount of that gas. This equation, which is shown below, can also be written using variables that have abbreviated or modified subscripts.

\( \dfrac{ \rm{V_{initial}}}{\rm{n_{initial}}} \) = \( \dfrac{ \rm{V_{final}}}{\rm{n_{final}}} \)

\( \dfrac{ \rm{V_{i}}}{\rm{n_{i}}} \) = \( \dfrac{ \rm{V_{f}}}{\rm{n_{f}}} \)

\( \dfrac{ \rm{V_{1}}}{\rm{n_{1}}} \) = \( \dfrac{ \rm{V_{2}}}{\rm{n_{2}}} \)

If the container in which the gas is held is rigid, rather than flexible, increasing the amount of gas that is present in that container causes the pressure of the gas to increase. Therefore, pressure can be substituted for volume in the less common representations of Avogadro's Law, which are shown below.

\( \dfrac{ \rm{P_{initial}}}{\rm{n_{initial}}} \) = \( \dfrac{ \rm{P_{final}}}{\rm{n_{final}}} \)

\( \dfrac{ \rm{P_{i}}}{\rm{n_{i}}} \) = \( \dfrac{ \rm{P_{f}}}{\rm{n_{f}}} \)

\( \dfrac{ \rm{P_{1}}}{\rm{n_{1}}} \) = \( \dfrac{ \rm{P_{2}}}{\rm{n_{2}}} \)