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?

The key to this problem lies with the definition of percent concentration by mass, `"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`.

`color(blue)("% m/m" = "mass of solute"/"mass of solution" xx 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 `"100 g"` of solution will contain `"3.62 g"` of sodium hypochlorite, your solute.

In your case, the mass of the solution is said to be equal to `"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

`"% m/m" = m_"solute"/m_"solution" xx 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