INSTRUCTOR: You're gonna
estimate the density of a mixture
that we obtained by mixing one liter of isopropyl alcohol
with three liters of water.
We gonna do this 20 degrees C,
and I've given
here the densities of these two species at 20 degrees C.
So there's different ways of doing this calculation.
We're going to assume that volumes are relative.
Some think that's a good approximation
for others it may not be,
but if we assume that then
the equation
that results in terms of density is
one over the density of the mixture
equals mass fraction
of one, the species isopropyl alcohol over its density,
its pure component density.
And then the mass fraction of water
over the density of water,
and all of these are at 20 degrees C.
So the first thing then we wanna do is calculate
the mass fractions.
And we're gonna do that by
using the density.
So if we have one liter,
isopropyl alcohol
I'm gonna
get things in the same unit.
So one liter is 10 to third, a thousand cubic centimeters.
And then the density
0.786 grams per cubic centimeter,
multiply that out 786 grams,
isopropyl alcohol in a liter.
And note
just to check
the units are consistent.
So now I'm going to do the same thing for water.
I'll pause, and do that
since it's the same type calculation.
So same calculation for water
we have three liters of water,
so we have a lot more mass of water.
And so now that I have the masses
I can calculate the mass fraction
of isopropyl alcohol,
786 grams of isopropyl alcohol,
and then the total
is the sum of these two.
So this mass fraction 0.208,
which means
the mass fraction of water is one minus 0.208.
.792.
So now I have
the densities,
the mass fractions I can go back to this equation,
and substitute.
So, what I'm gonna do is
one over the density of the mixture,
So mass fraction of isopropyl alcohol
density 0.786,
grams per cubic centimeter,
and then the same mass fraction of water,
density 998 grams per cubic centimeter.
And I do the calculation
one over the density is
so this would be the specific volume,
and therefore the inverse of that,
the density then
is one over 1.058.
And that's 0.945 grams per cubic centimeter.
So that's a density of mixture,
mix one liter of isopropyl alcohol,
and three liters of water.