Question 4.4: Solutions of Known Concentration To analyze the alcohol cont...

Where are we going?
We are asked to determine the mass of K_{2} CrO_{7} solute required to make 1.00 L of a 0.200 M solution.

What do we know?
We are given the concentration and volume of solution, along with the molecular formula of the compound.

What information do we need?
We need to determine the moles of the solid.

How do we get there?
Knowing that molarity is a ratio of moles of solute to liters of solution, we can use molarity and volume to determine the moles of solute.

M=  \frac{moles   of   solute }{liters   of   solution}

Thus

Moles =  M × volume

However, we are asked for mass, so we will need to convert the moles to a mass, and we can do this using the molar mass of the solute.
First, determine the moles of K_{2} Cr_{2}O_{7}   required:

1.00   L   solution × \frac{0.200   mol  K_{2} Cr_{2}O_{7}}{L   solution } =  0.200   mol  K_{2} Cr_{2}O_{7}

This amount can be converted to grams by using the molar mass of K_{2} Cr_{2}O_{7}  :

  0.200   mol  K_{2} Cr_{2}O_{7} × \frac{294.2  g  K_{2} Cr_{2}O_{7} }{mol  K_{2} Cr_{2}O_{7}} =  58.8  g  K_{2} Cr_{2}O_{7}

Thus, to make 1.00 L of 0.200 M K_{2} Cr_{2}O_{7} , the chemist must weigh out 58.8 g of K_{2} Cr_{2}O_{7} , put it in a 1.00-L volumetric flask, and add water up to the mark on the flask.
Note: In looking back at the solutions to Examples 4.1 through 4.4, you should notice that the problems are solved similarly. For example, in all cases we need to know what molarity means and how to manipulate the formula for concentration. The problems vary in the details. In Examples 4.1, 4.3, and 4.4, we need to use molar mass = mass/mol. In Example 4.2, we need to understand how an ionic solid dissolves. As discussed in Section 3.4, we need to ask questions that allow the problem to guide us, but we also need a bank of knowledge to draw from.