# You have 1500.0 g of a bleach solution. The percent by mass of the solute sodium hypochlorite, NaOCl, is 3.62%. How many grams of NaOCl are in the solution?

Jan 17, 2016

$\text{54.3 g NaOCl}$

#### Explanation:

The key to this problem lies with the definition of percent concentration by mass, $\text{m/m %}$.

As you know, percent concentration by mass is defined as the ratio between the mass of the solute and the total mass of the solution, multiplied by $100$.

$\textcolor{b l u e}{\text{% m/m" = "mass of solute"/"mass of solution} \times 100}$

You are told that your bleach solution has a "3.62% percent concentration by mass. Looking at the above definition, that should tell you that every $\text{100 g}$ of solution will contain $\text{3.62 g}$ of sodium hypochlorite, your solute.

In your case, the mass of the solution is said to be equal to $\text{1500.0 g}$. This means that it will contain

1500.0 color(red)(cancel(color(black)("g solution"))) * "3.62 g NaOCl"/(100color(red)(cancel(color(black)("g solution")))) = color(green)("54.3 g NaOCl")

Alternatively, you can use the equation for percent concentration by mass to find the mass of the solute

$\text{% m/m" = m_"solute"/m_"solution} \times 100$

m_"solute" = ("%m/m" * m_"solution")/100

Plug in your values to get

m_"solute" = (3.62 * "1500.0 g")/100 = color(green)("54.3 g NaOCl")

Here's a useful video on percent concentration by mass