# 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?

##### 1 Answer

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# ,

where **molar density**,

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**, *nonideal* gases given their molar masses.

Given

#"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* *which is* *Can you figure out how to get the answer of* *of* *in* *of* *?*