Question

What volume of solution must be added to 4.0 mol of NaCl to make a 1.2 M solution?

Answer 1

`\boxed {\boxed {\sf 3.3 \ liters}}}`

Step-by-step explanation:

Molarity is a measure of concentration in moles per liter.

`molarity=(moles \ of \ solute)/(liters \ of \ solution)}`

The solution has a molarity of 1.2 M or 1.2 moles per liter. There are 4.0 moles of NaCl, the solute. We don't know the liters of solution, so we can use x.

• molarity= 1.2 mol/L
• moles of solute= 4.0 mol
• liters of solution =x

Substitute the values into the formula.

`1.2 \ mol/L = (4.0 \ mol)/(x)`

Since we are solving for x, we must isolate the variable. Begin by cross multiply (multiply the 1st numerator and 2nd denominator, then the 1st denominator and 2nd numerator.

`\frac {1.2 \ mol/L}{1}=( 4.0 \ mol)/(x)`

`4.0 \ mol *1=1.2 \ mol/L *x`

`4.0 \ mol = 1.2 \ mol/L *x`

x is being multiplied by 1.2 moles per liter. The inverse of multiplication is division, so divide both sides by 1.2 mol/L

`(4.0 \ mol)/(1.2 \ mol/L) = (1.2 \ mol/L *x)/(1.2 \ mol/L)`

`(4.0 \ mol)/(1.2 \ mol/L)=x`

The units of moles (mol) will cancel.

`(4.0 )/(1.2 ) \ L =x`

`3.33333333 \ L=x`

The original measurements both have 2 significant figures, so our answer must have the same. For the number we found, this is the tenths place.

The 3 in the hundredth place tells us to leave the 3 in the tenths place.

`3.3 \ L\approx x`

Approximately 3.3 liters of solution are needed to make a 1.2 M solution with 4.0 moles of sodium chloride.