Question

A 50.0 gram sample of NaOH is dissolved in 0.600 L of water. What volume of this solution would be needed to create a 1.50 L solution that is 0.200 M NaOH?

Answer 1

0.144 L (144 mL).

Step-by-step explanation:

First, let's calculate the molarity of the solution of 0.600 L of water with 50.0 g of NaOH. But first, let's calculate the number of moles of 50.0 g of NaOH using its molar mass which is 40 g/mol (you can calculate the molar mass of a compound using the periodic table):

`50.0\text{ g NaOH}\cdot\frac{1\text{ mol NaOH}}{4\text{0 g NaOH}}=1.25\text{ moles NaOH.}`

The next step is to use the formula of molarity:

`Molarity\text{ \lparen M\rparen=}\frac{mole\text{s of solute}}{liter\text{s of solution}}=(mol)/(L).`

And replace the given data (moles of solute = 1.25, liters of solution = 0.600 L):

`Molarity=\frac{1.25\text{ moles}}{0.600\text{ L}}=2.08\text{ M.}`

We want to find the volume that is needed to create a 1.50 L (volume) of 0.200 M NaOH. We have to use the formula:

`C_1V_1=C_2V_2.`

Where C indicates the concentration in M and V the volume in L. In this case, our unknown value can be V1 but remember that the concentration of this solution (C1) was 2.08 M and we have to equal this to the concentration (0.200 M) and volume (1.50 L) of the wanted solution. It will look like this:

`V_1=(C_2V_2)/(C_1)=\frac{0.200\text{ M}\cdot1.50L}{2.08\text{ M}}=0.144\text{ L.}`

The volume required would be 0.144 L (144 mL).