# Question 5ab50

Aug 31, 2016

color(orange)("1.1 g/mL"

#### Explanation:

To calculate the density of the solution, we have to use the formula below:

$\textcolor{b l u e}{\text{Density")= color(red)(" (Mass)/(Volume)}}$

• Usually, density will have units of $\frac{g}{m L}$ when dealing with a liquid or units of $\frac{g}{c {m}^{3}}$ when dealing with a solid.

• The mass has units of grams, $g$.

• The volume can have units of milliliters, $m L$

Let's determine the mass of the solution:

Mass of solution = mass of solute + mass of solvent

color(red)("solvent:" 73 cancel "mL" xx (1g)/(cancel"mL")#= 73g

( I used the density of water, 1 g/mL, to determine the mass of solvent.)

The mass of solute (23 g) is already given, so we add the two values together to obtain the mass of the solution:

$23 g + 73 g = 96 g$

Now, we need the volume of solution:

Volume of solution = volume of solute + volume of solvent:

$\textcolor{b l u e}{\text{solute:}}$ $23 \cancel{g} \times \frac{1 m L}{2.165 \cancel{g}}$ = 10.62 mL

( I used the density of table salt, 2.165 g/mL, to determine the volume of the solute)

The volume of solvent (73mL) is already provided, so the total volume of the solution is:

$10.62 m L + 73 m L = 83.62 m L$

Divide the mass of the solution by the volume of the solution to obtain the density:

Density = $\frac{96 g}{83.62 m L}$ = 1.1 g/mL