Question

An oven-cleaning solution is 40.0% (by mass) `NaOH`. If one jar of this product contains 454 g of solution, how much `NaOH` does it contain?

Answer 1

`182 "g NaOH"`

Explanation:

We're asked to find how much `"NaOH"` is in a `454"g"` solution containing `40% "NaOH"` by mass.

#40% in decimal form is

`(40.0cancel(%))/(100cancel(%)) = 0.400`

(you probably already know this, but it keeps calculations a little simpler:)

To find how much `"NaOH"` is in the solution, we take this fraction `(0.400)`, and multiply it by the total mass of the solution:

Mass `"NaOH" = (0.400)(454"g") = color(red)(182"g NaOH"`

rounded to three significant figures, the amount given in the question.

You could also report this in moles of sodium hydroxide, using its molar mass to calculate the number of moles:

`182 cancel("g NaOH")((1 "mol NaOH")/(40.00 cancel("g NaOH"))) = color(blue)(4.55 "mol NaOH"`

However, since the amount of a substance is most often expressed in grams (because you can measure mass directly, but can't necessarily measure moles directly), it's more conventional to report your answer in grams, unless it says otherwise.