Answer:
[tex]\boxed {\boxed {\sf 3.3 \ liters}}}[/tex]
Explanation:
Molarity is a measure of concentration in moles per liter.
[tex]molarity=\frac{moles \ of \ solute}{liters \ of \ solution}}[/tex]
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.
[tex]1.2 \ mol/L = \frac{4.0 \ mol}{x}[/tex]
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.
[tex]\frac {1.2 \ mol/L}{1}=\frac{ 4.0 \ mol}{x}[/tex]
[tex]4.0 \ mol *1=1.2 \ mol/L *x[/tex]
[tex]4.0 \ mol = 1.2 \ mol/L *x[/tex]
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
[tex]\frac{4.0 \ mol}{1.2 \ mol/L} = \frac{1.2 \ mol/L *x}{1.2 \ mol/L}[/tex]
[tex]\frac{4.0 \ mol}{1.2 \ mol/L}=x[/tex]
The units of moles (mol) will cancel.
[tex]\frac{4.0 }{1.2 } \ L =x[/tex]
[tex]3.33333333 \ L=x[/tex]
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.
[tex]3.3 \ L\approx x[/tex]
Approximately 3.3 liters of solution are needed to make a 1.2 M solution with 4.0 moles of sodium chloride.
