Question

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

Answer 1

Answer:

$\boxed {\boxed {\sf 3.3 \ liters}}}$

Explanation:

Molarity is a measure of concentration in moles per liter.

$molarity=\frac{moles \ of \ solute}{liters \ of \ solution}}$

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.

$1.2 \ mol/L = \frac{4.0 \ mol}{x}$

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.

$\frac {1.2 \ mol/L}{1}=\frac{ 4.0 \ mol}{x}$

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

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

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

$\frac{4.0 \ mol}{1.2 \ mol/L} = \frac{1.2 \ mol/L *x}{1.2 \ mol/L}$

$\frac{4.0 \ mol}{1.2 \ mol/L}=x$

The units of moles (mol) will cancel.

$\frac{4.0 }{1.2 } \ L =x$

$3.33333333 \ L=x$

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.