Question

What volume (in liters) of a solution contains 0.14 mol of KCl?

1.8 M KCl
Express your answer using two significant figures.

Answer 1

`\boxed {\boxed {\sf 0.078 \ L }}`

Step-by-step 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:

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

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.

`1.8 \ mol \ KCl/ L = \frac { 0.14 \ mol \ KCl}{x}`

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.

`\frac {1.8 \ mol \ KCl/L}{1} = (0.14 \ mol \ KCl)/(x)`

`1.8 \ mol \ KCl/ L *x = 1*0.14 \ mol \ KCl`

`1.8 \ mol \ KCl/ L *x = 0.14 \ mol \ KCl`

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.

`\frac {1.8 \ mol \ KCl/ L *x}{1.8 \ mol \ KCl/L} = (0.14 \ mol \ KCl)/(1.8 \ mol \ KCl/L)`

`x= (0.14 \ mol \ KCl)/(1.8 \ mol \ KCl/L)`

The units of moles of potassium chloride cancel.

`x= (0.14 )/(1.8 L)`

`x=0.07777777778 \ L`

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.

`x \approx 0.078 \ L`

There are approximately 0.078 liters of solution.