Given that the molar mass of NaCl 58.44 g/mol, what is the molarity of a solution that contains 87.75 g of NaCl in 500. mL of solution?

Question

Natalie Anton · Accepted Answer

#"3.00 mol L"^(-1)#

Molarity is a measure of how many moles of solute you get in exactly #"1 L"# of a given solution.

The objective is to determine the number of moles in the sample using the molar mass of sodium chloride.

#87.75 color(red)(cancel(color(black)("g"))) * "1 mole NaCl"/(58.44color(red)(cancel(color(black)("g")))) = "1.5015 moles NaCl"#

Now, you know that this solution contains #1.5015# moles of sodium chloride, the solute, in #"500. mL"# of solution. Since

#500.0 color(red)(cancel(color(black)("mL"))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = "0.500 L"#

you can use this known composition of the solution as a conversion factor to help you find the number of moles of solute present in #"1 L"# of solution

#1 color(red)(cancel(color(black)("L solution"))) * "1.5015 moles NaCl"/(0.500color(red)(cancel(color(black)("L solution")))) = "3.003 moles NaCl"#

At this point, the solution's molarity can be stated as

#color(darkgreen)(ul(color(black)("molarity = 3.00 mol L"^(-1))))#

The number of sig figs you have for the volume of the solution is the answer, which is rounded to three.

Natalie Anton · Answer

undefined To find the molarity of the solution, first, calculate the number of moles of NaCl using the formula: 
Number of moles = Mass of solute (in grams) / Molar mass of solute (in g/mol)
Number of moles of NaCl = 87.75 g / 58.44 g/mol = 1.5 mol
Then, calculate the volume of the solution in liters:
Volume of solution = 500 mL / 1000 mL/L = 0.5 L
Finally, use the formula for molarity:
Molarity = Number of moles of solute / Volume of solution (in liters)
Molarity = 1.5 mol / 0.5 L = 3.0 M