### Video Transcript

What is the molarity of a solution
made by dissolving 21.5 grams of sodium sulfate, Na2SO4, in enough water to form 150
milliliters of solution? Give your answer to three decimal
places. The molar mass of oxygen is 16
grams per mole, sodium is 23 grams per mole, and sulfur is 32 grams per mole.

Molarity, or molar concentration,
is one of several ways to express the quantitative amount of solute in a
solution. More specifically, molarity
expresses the number of moles of solute per liter of solution. The molarity of a solution can be
calculated using the equation π equals π divided by π£, where π is the molarity
in moles per liter, π is the amount of solute in moles, and π£ is the volume of the
solution in liters.

In the question, we are told that
21.5 grams of sodium sulfate are dissolved in water to form the solution. Since sodium sulfate is the
substance being dissolved, it is the solute in this solution. We have been given the mass of the
solute in grams, but we need to know the amount of solute in moles. We can use the equation π equals
lowercase π divided by capital π to convert the mass in grams into an amount in
moles. In this equation, π is the amount
in moles, lowercase π is the mass in grams, and capital π is the molar mass in
grams per mole. We know the mass, but we have not
been given the molar mass of sodium sulfate. We have been given the average
molar mass of oxygen, sodium, and sulfur. We can use these values to
calculate the molar mass of sodium sulfate.

One formula unit of sodium sulfate
contains two atoms of sodium, one atom of sulfur, and four atoms of oxygen. Each sodium atom has an average
molar mass of 23 grams per mole. So two sodium atoms will have an
average molar mass of 46 grams per mole. One sulfur atom has an average
molar mass of 32 grams per mole. One oxygen atom has an average
molar mass of 16 grams per mole, so four oxygen atoms will have an average molar
mass of 64 grams per mole. Adding these molar masses together
gives us the molar mass of sodium sulfate, 142 grams per mole.

Now, we can substitute the mass and
molar mass into the equation. The grams unit will cancel, leaving
us with a unit of moles. Performing the calculation gives us
an amount of 0.1514 moles. We now know the value of π in the
molarity equation. The question tells us that the
volume of the solution is 150 milliliters. But in order to solve for molarity,
the volume must be given in liters. We can convert between the two
volume units by using the relationship one liter is equal to 1000 milliliters.

To perform the conversion, we can
multiply the 150 milliliters given in the question by the relationship written as a
fraction with the unit milliliters in the denominator so that the milliliter units
cancel. Performing the calculation gives us
a volume of 0.15 liters. Now that we have values for both π
and π£, we can solve for the molarity. Dividing 0.1514 moles by 0.15
liters gives us a molarity of 1.00939 moles per liter. The question tells us to give our
answer to three decimal places.

So, to three decimal places, the
molarity of a solution made by dissolving 21.5 grams of sodium sulfate in enough
water to form 150 milliliters of solution is 1.009 moles per liter.