To 225 mL of a 0.80M solution of #KI#, a student adds enough water to make 1.0 L of a more dilute #KI# solution. What is the molarity of the new solution?

Question

Wyatt Adkins · Accepted Answer

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

Diluting a solution means, as you already know, that the molarity of the solution decreased when water was added.

The idea behind a dilution is that by increasing a solution's volume while maintaining a constant number of moles of solute, you can lower the solution's concentration.

So, you can use the molarity and volume of the initial solution to find the number of moles of potassium iodide, #"KI"#, present in the solution

#color(purple)(|bar(ul(color(white)(a/a)color(black)(c = n_"solute"/V_"solution" implies n_"solute" = c * V_"solution")color(white)(a/a)|)))#

Keep in mind that molarity works with liters of solution, so don't forget to convert the milliliter volume to liters.

#n_(KI) = "0.80 mol" color(red)(cancel(color(black)("L"^(-1)))) * 225 * 10^(-3)color(red)(cancel(color(black)("L"))) = "0.180 moles KI"#

You can say that because this is the precise number of moles of solute that must be present in the diluted solution.

#c_"diluted" = n_(KI)/V_"solution"#

#c_"diluted" = "0.180 moles"/"1.0 L" = color(green)(|bar(ul(color(white)(a/a)"0.18 mol L"^(-1)color(white)(a/a)|)))#

This is precisely what you can accomplish using the dilution calculation formula.

#color(blue)(overbrace(c_1 xx V_1)^(color(black)("moles of solute in initial solution")) = overbrace(c_2 xx V_2)^(color(black)("moles of solute in diluted solution")))#

Here

#c_1#, #V_1# - the molarity and volume of the initial solution #c_2#, #V_2# - the molarity and volume of the diluted solution

Enter your values to obtain

#c_2 = V_/1V_2 * c_1#

#c_2 = (225 * 10^(-3)color(red)(cancel(color(black)("L"))))/(1.0color(red)(cancel(color(black)("L")))) * "0.80 mol L"^(-1) = color(green)(|bar(ul(color(white)(a/a)"0.18 mol L"^(-1)color(white)(a/a)|)))#

Two sig figs are used to round the result.

Caleb Adams · Answer

undefined The molarity of the new solution is 0.18 M.