### Video Transcript

A student wants to prepare a
0.1-molar solution of silver nitrate, AgNO3, in a volumetric flask that can contain
100 milliliters of water. How much silver nitrate does the
student need to dissolve? Give your answer to one decimal
place.

The molar mass of nitrogen is 14
grams per mole, oxygen is 16 grams per mole, and silver is 108 grams per mole. In this question, a student is
going to prepare a solution of silver nitrate in a volumetric flask that is designed
to contain 100 milliliters of solution. The solute of the solution is solid
silver nitrate, and the student will need to use a balance to measure the mass in
grams. After adding the solid silver
nitrate to the flask, the student will dissolve the solid silver nitrate in water,
which is the solvent, and add enough water to the flask to reach a final volume of
100 milliliters of solution. We are told that the final
concentration of the silver nitrate solution must be 0.1 molar. Our job in solving this problem is
to determine the amount of silver nitrate in grams that the student must dissolve in
water to make the 0.1-molar solution of silver nitrate.

The molar concentration, or
molarity, of a solution is a measure of the number of moles of solute per liter of
solution. In this problem, the units of
molarity are written as a capital M. However, the units moles per liter
are also often written to represent molarity.

During our problem-solving process,
weโll need to make use of the molarity equation. In this equation, ๐ is the number
of moles of solute, ๐ is the molarity of the solution in moles per liter, and ๐ฃ is
the volume of the solution in liters. Before we can use the molarity
equation, we need to convert the 100 milliliters of solution to liters. Then, we can substitute the molar
concentration and volume of the solution into the equation to determine the amount
of moles of silver nitrate. Our last step will be to convert
the amount of moles of AgNO3 to grams.

Letโs begin by converting the
volume of the solution from milliliters to liters. There are 1000 milliliters per one
liter. To perform the conversion, we will
need to multiply the volume of the solution, which is 100 milliliters, by one liter
per 1000 milliliters. The result is 0.1 liters.

Now, weโre ready to substitute the
concentration of the solution and the volume of the solution into the molarity
equation. We can write ๐ equals 0.1 moles
per liter multiplied by 0.1 liters. The result is 0.01 moles, which is
the amount of moles of AgNO3. Because the amount in moles of a
substance cannot be directly measured using a laboratory balance, we now need to
convert the amount of moles of silver nitrate to grams.

We can make use of the following
equation to help us. In this equation, ๐ is the number
of moles, lowercase ๐ is the mass in grams, and capital ๐ is the molar mass in
grams per mole. We will need to calculate the molar
mass of silver nitrate first before we can use the equation.

The molar mass of silver nitrate
can be calculated by adding together the average molar masses of the atoms that make
up a formula unit of silver nitrate. One formula unit of silver nitrate
is composed of one silver atom, one nitrogen atom, and three oxygen atoms. Next, we need to multiply the
number of each type of atom by the average molar masses of the atoms, which are
provided in the problem. After adding together the results
of these calculations, we get an answer of 170 grams per mole, which is the molar
mass of silver nitrate.

Now, weโre ready to substitute the
amount of moles of silver nitrate, which was our answer from step two, and the molar
mass of silver nitrate into the equation. We can write 0.01 moles equals
lowercase ๐ divided by 170 grams per mole. We can rearrange the equation to
solve for ๐. We get ๐ equals 170 grams per mole
multiplied by 0.01 moles. After multiplying, the result is
1.7 grams. The student will need to dissolve
1.7 grams of silver nitrate to produce 100 milliliters of a 0.1-molar solution of
silver nitrate.