If we have #"24.9 L"# of liquid ethanol, with a density of #"789 g/L"# at a certain temperature, how many mols do we have?
Let's consider the ideal gas law for a moment, for a transition point.
#P\mathbf(V) = \mathbf(n)RT#
Notice how we can divide by
#P\mathbf(barV) = RT#,
Obviously the ideal gas law is not supposed to work for liquids (liquid isn't even in the name), so what do we use instead of the molar density, which is really just the reciprocal molar volume?
The mass density,
#"mol" = cancel"L" xx cancel"g"/cancel"L" xx "mol"/cancel"g" = Vxxrhoxx1/M_r#,
so we see the calculation goes as follows:
#=> 24.9 cancel"L EtOH" xx (789cancel"g EtOH")/cancel"L EtOH" xx "mol EtOH"/(46.07cancel"g EtOH")#,
#~~# #color(blue)("372 mol EtOH")#
You can see at this point that the ideal gas law would clearly fail for a liquid. That's because of the significantly higher density than many gases. Generally liquids are approximately
CHALLENGE: An example of the density of a typical ideal gas is