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.