Question #cb5de

In order to find the mole fraction of potassium chloride, #"KCl"#, in your solution, you must first find the mass of potassium chloride and the mass of water present in a sample of this solution.

To do that, you must pick a sample of this solution and calculate how many grams of potassium chloride, the solute, and how many grams of water, the solvent, it contains.

The problem provides you with the mass by mass percent concentration, #"% m/m"#, of the solution. By definition, the mass by mass percent concentration tells you how many grams of solute you have in #"100 g"# of solution.

In this case, a #23% "m/m"# potassium chloride solution will contain #"23.3 g"# of potassium chloride for every #"100 g"# of solution.

This means that if you pick a #"100.0g"# sample of this solution, you will get

#m_"KCl" = "23.3 g"#

and

#m_"water" = "100.0 g" - "23.3 g" = "76.7 g water"#

To convert these masses into moles, use the molar masses of the two compounds

#23.3 color(red)(cancel(color(black)("g"))) * "1 mole KCl"/(74.55 color(red)(cancel(color(black)("g")))) = "0.31254 moles KCl"#

#76.7 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "4.25756 moles H"_2"O"#

The mole fraction of potassium chloride, #chi_"KCl"#, is equal to the number of moles of potassium chloride divided by the total number of moles present in solution.

You will thus have

#chi_"KCl" = (0.31254 color(red)(cancel(color(black)("moles"))))/((0.31254 + 4.25768)color(red)(cancel(color(black)("moles")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(0.0684)color(white)(a/a)|)))#

The answer is rounded to three sig figs.