# What is the molarity of a salt solution made by dissolving 240mg of NaCl in 4ml of water? Assume final volume is the same as the volume of water.

Jun 17, 2017

${\text{1 mol L}}^{- 1}$

#### Explanation:

In order to find the molarity of the solution, you must determine the number of moles of solute present in exactly

$\text{1 L} = {10}^{3}$ $\text{mL}$

of solution. Notice that you already know the number of milligrams of sodium chloride, the solute, present in $\text{4 mL}$ of solution, so start by calculating the mass of solute present in ${10}^{3}$ $\text{mL}$ of solution.

10^3 color(red)(cancel(color(black)("mL solution"))) * "240 mg NaCl"/(4color(red)(cancel(color(black)("mL solution")))) = 60 * 10^3 $\text{mg}$

Since

color(blue)("1 g" = 10^3color(white)(.)"mg"

you can say that ${10}^{3}$ $\text{mL}$ of solution contain

$60 \cdot \textcolor{b l u e}{{10}^{3} \textcolor{w h i t e}{.} \text{mg") = 60color(white)(.)color(blue)("g}}$

of sodium chloride. Now, to convert this to moles, use the molar mass of the compound

60 color(red)(cancel(color(black)("g"))) * "1 mole NaCl"/(58.44color(red)(cancel(color(black)("g")))) = "1.027 moles NaCl"

Since this represents the number of moles of sodium chloride present in ${10}^{3}$ $\text{mL}$ of solution, you can say that the molarity of the solution is equal to

color(darkgreen)(ul(color(black)("molarity = 1 mol L"^(-1)))

The answer must be rounded to one significant figure, the number of sig figs you have for the volume of the solution.

Jun 17, 2017

M=$\text{1 mol/L}$

#### Explanation:

The molarity of a solution is the concentration of moles of solute per liter of solution, $\text{mol/L}$. The mass of $\text{NaCl}$ must be converted to grams and then moles. The volume of the solution must be converted to liters.

Convert $\text{mg NaCl}$ to $\text{g NaCl}$.

$\text{1 g=1000 mg}$

240color(red)cancel(color(black)("mg NaCl"))xx(1"g")/(1000color(red)cancel(color(black)("mg")))="0.24 g NaCl"

Determine moles of $\text{NaCl}$.

Divide the mass of $\text{NaCl}$ by its molar mass by multiplying by its inverse.

Molar mass $\text{NaCl=58.44 g/mol}$

0.24color(red)cancel(color(black)("g NaCl"))xx(1"mol NaCl")/(58.44color(red)cancel(color(black)("g NaCl")))="0.0041 mol NaCl"

Molarity of $\text{NaCl}$.

Convert $\text{4 mL}$ to liters.

$\text{1 L=1000 mL}$

4color(red)cancel(color(black)("mL"))xx(1"L")/(1000color(red)cancel(color(black)("mL")))="0.004 L"

Divide mol NaCl by volume of solution.

$\text{M"=(0.0041"mol NaCl")/(0.004"L solution")="1 mol/L}$ rounded to one sig fig due to $4$ mL