What is molarity of a solution containing 7 g of NaOH in 500 mL of NaOH solution?

Molarity is defined as moles of solute, which in your case is sodium hydroxide, #"NaOH"#, divided by liters of solution.

#color(blue)("molarity" = "moles of solute"/"liters of solution")#

Notice that the problem provides you with the volume of the solution, but that the volume is expressed in milliliters, #"mL"#.

Moreover, you don't have the number of moles of sodium hydroxide, you just have the mass in grams. So, your strategy here will be to

• determine how many moles of sodium hydroxide you have in that many grams
• convert the volume of the solution from milliliters to liters

So, to get the number of moles of solute, use sodium hydroxide's molar mass, which tells you what the mass of one mole of sodium hydroxide is.

#7color(red)(cancel(color(black)("g"))) * "1 mole NaOH"/(40.0color(red)(cancel(color(black)("g")))) = "0.175 moles NaOH"#

The volume of the solution in liters will be

#500color(red)(cancel(color(black)("mL"))) * "1 L"/(1000color(red)(cancel(color(black)("mL")))) = "0.5 L"#

Therefore, the molarity of the solution will be

#color(blue)(c = n/V)#

#c = "0.175 moles"/"0.5 L" = "0.35 M"#

Rounded to one sig fig, the answer will be

#c = color(green)("0.4 M")#