Question #1c29c

A solution's molar concentration, or molarity, tells you the number of moles of solute, which in your case is sodium hydroxide, `"NaOH"`, present in exactly `"1 L"` of the solution.

You know that your solution has a concentration of `"15 g L"^(-1)` sodium hydroxide, which means that `"1 L"` of this solution contains `"15 g"` of sodium hydroxide.

Now, in order to convert the number of grams of sodium hydroxide present in `"1 L"` of this solution to moles, you need to use the molar mass of sodium hydroxide.

The problem provides you with the molar masses of its constituent elements

• `"Na" = "23 g mol"^(-1)`
• `"O" = "16 g mol"^(-1)`
• `"H" = "1 g mol"^(-1)`

to find the molar mass of the compound. Since `1` mole of sodium hydroxide contains `1` mole of sodium, `1` mole of oxygen, and `1` mole of hydrogen, you can say that the molar mass of sodium hydroxide is equal to

`"23 g mol"^(-1) + "16 g mol"^(-1) + "1 g mol"^(-1) = "40 g mol"^(-1)`

This tells you that `1` mole of sodium hydroxide has a mass of `"40 g"`.

You can thus say that the number of moles of sodium hydroxide present in `"1 L"` of solution will be

`15 color(red)(cancel(color(black)("g"))) * "1 mole NaOH"/(40color(red)(cancel(color(black)("g")))) = "0.375 moles NaOH"`

Therefore, the molarity of the solution will be

`color(darkgreen)(ul(color(black)("molarity = 0.38 mol L"^(-1))))`

I'll leave the answer rounded to two sig figs, the number of sig figs you have for the concentration in grams per liter.