Answer:
[tex]\boxed {\boxed {\sf 0.078 \ L }}[/tex]
Explanation:
We are asked to find the volume of a solution given the moles of solute and molarity.
Molarity is a measure of concentration in moles per liter. It is calculated using the following formula:
[tex]molarity= \frac{moles \ of \ solute}{liters \ of \ solution}[/tex]
We know there are 0.14 moles of potassium chloride (KCl), which is the solute. The molarity of the solution is 1.8 molar or 1.8 moles of potassium chloride per liter.
- moles of solute = 0.14 mol KCl
- molarity= 1.8 mol KCl/ L
- liters of solution=x
Substitute these values/variables into the formula.
[tex]1.8 \ mol \ KCl/ L = \frac { 0.14 \ mol \ KCl}{x}[/tex]
We are solving for x, so we must isolate the variable. First, cross multiply. Multiply the first numerator and second denominator, then the first denominator and second numerator.
[tex]\frac {1.8 \ mol \ KCl/L}{1} = \frac{0.14 \ mol \ KCl}{x}[/tex]
[tex]1.8 \ mol \ KCl/ L *x = 1*0.14 \ mol \ KCl[/tex]
[tex]1.8 \ mol \ KCl/ L *x = 0.14 \ mol \ KCl[/tex]
Now x is being multiplied by 1.8 moles of potassium chloride per liter. The inverse operation of multiplication is division, so we divide both sides by 1.8 mol KCl/L.
[tex]\frac {1.8 \ mol \ KCl/ L *x}{1.8 \ mol \ KCl/L} = \frac{0.14 \ mol \ KCl}{1.8 \ mol \ KCl/L}[/tex]
[tex]x= \frac{0.14 \ mol \ KCl}{1.8 \ mol \ KCl/L}[/tex]
The units of moles of potassium chloride cancel.
[tex]x= \frac{0.14 }{1.8 L}[/tex]
[tex]x=0.07777777778 \ L[/tex]
The original measurements of moles and molarity have 2 significant figures, so our answer must have the same. For the number we found, that is the thousandth place. The 7 in the ten-thousandth place tells us to round the 7 up to a 8.
[tex]x \approx 0.078 \ L[/tex]
There are approximately 0.078 liters of solution.
