# How many liters of a 0.2 M NaOH solution are needed in order to have 1.0 moles of NaOH?

Oct 17, 2016

$\text{5 litres}$ of solution are required.

#### Explanation:

$\text{Concentration}$ $=$ $\text{Moles of solute"/"Volume of solution}$.

Given that the typical units of $\text{concentration}$ are $m o l \cdot {L}^{-} 1$, to get $\text{concentration}$ or $\text{amount of moles}$ or $\text{volume of solution}$ we just have to take the appropriate product or quotient.

We want $1.0 \cdot m o l$ $N a O H$:

this the product $\text{Volume of solution "xx" Concentration}$.

So we need the quotient: $\text{Moles of solute"/"Concentration}$ $=$ $\frac{1.0 \cdot \cancel{m o l}}{0.2 \cdot \cancel{m o l} \cdot {L}^{-} 1}$ $=$ $5 \cdot L$.

(i.e. 1/(1*L^-1)=1*L)

Note that we go to such trouble in including the units in these calculations as an extra check on our arithmetic. Sometimes you ask yourself should I divide or should I multiply. Dimensional analysis answers our question. We wanted an answer in $\text{litres}$, and we got one. This persuades us that we did the calculation right.