# How do you calculate the number of grams of substance needed to make the following solution: 50 "cm"^3 of "NaOH (aq)", concentration 2 "mol" "dm"^-3?

Dec 25, 2016

#### Answer:

Here's how you can do that.

#### Explanation:

Start by calculating how many moles of sodium hydroxide you need in order to have ${\text{50 cm}}^{3}$ of ${\text{2 mol dm}}^{- 3}$ solution.

As you know, molarity is defined as the number of moles of solute, which in this case is sodium hydroxide, present in ${\text{1 dm}}^{3}$ of solution.

This means that a ${\text{2 mol dm}}^{- 3}$ solution will have $2$ moles of sodium hydroxide dissolved for every ${\text{1 dm}}^{3}$ of solution. In your case, the sample must contain

50 color(red)(cancel(color(black)("cm"^3"solution"))) * (1color(red)(cancel(color(black)("dm"^3))))/(10^3color(red)(cancel(color(black)("cm"^3"solution")))) * "2 moles NaOH"/(1color(red)(cancel(color(black)("dm"^3"solution"))))

$= \text{ 0.10 moles NaOH}$

Now, in order to convert this to grams of sodium hydroxide, use the compound's molar mass. You will end up with

$0.10 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles NaOH"))) * "40.0 g"/(1color(red)(cancel(color(black)("mole NaOH")))) = color(darkgreen)(ul(color(black)("4 g}}}}$

The answer must be rounded to one significant figure.