# Introduction to Chemical Engineering Processes/Unusual Units

## Standard vs. Actual Volume

When specifying the volume of a gas, the pressure and temperature must be specified because the volume of a gas depends strongly on both temperature and pressure (assuming that it is in an expandable container). In order to avoid specifying a different set of conditions for each measurement, an engineer can convert to standard temperature and pressure (typically 1 atm and 0oC) which is common to all measurements. This allows direct comparisons of volume measurements, but also requires that one convert back to the actual conditions present in the system before the value can be used.

The conversion that is used assumes that the gas is ideal, so that:

$PV=nRT$

### Conversion of volume to volume

We wish to compare a standard state to the actual state in the system. Let us consider the standard state (state "s") first. We have the ideal gas law for the standard state:

$P_{s}*V_{s}=n_{s}RT_{s}$

Now let us compare the standard state to the actual conditions in the system. The standard state conditions have been completely specified. The ideal gas law is assumed to hold in the actual system conditions as well:

$P_{a}V_{a}=n_{a}RT_{a}$

Divide this equation by the standard-state ideal gas law gives:

${\frac {P_{a}V_{a}}{P_{s}{V}_{s}}}={\frac {n_{a}RT_{a}}{n_{s}RT_{s}}}$

where a is actual and s is standard. If we assume that we want to compare the same number of moles of the substance between the standard and actual states, the following conversion between the states is obtained:

Conversion from standard to actual volume

$V_{a}={\frac {P_{s}V_{s}}{T_{s}}}*{\frac {T_{a}}{P_{a}}}$