Question #f9869
1 Answer
Here's what I got.
Explanation:
The idea here is that you need to use the molarity of the three solutions to write two equations that establish a relationship between the number of moles of hydrochloric acid and the volumes of the solutions.
As you know, molarity is defined as the number of moles of solute, which in your case is hydrochloric acid, you get per liter of solution.
Use the molarity and volume of the target solution to determine how many moles of hydrochloric acid it must contain
#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)|)))#
You will end up with
#n_(HCl) = "0.2 mol" color(red)(cancel(color(black)("L"^(-1)))) * 2 color(red)(cancel(color(black)("L"))) = "0.40 moles HCl"#
Now, let's assume that you must mix
The number of moles of hydrochloric acid coming from solution
#x color(red)(cancel(color(black)("L"))) * "0.5 moles HCl"/(1color(red)(cancel(color(black)("L")))) = (0.5x)color(white)(a)"moles HCl"#
The number of moles of hydrochloric acid coming from solution
#y color(red)(cancel(color(black)("L"))) * "0.1 moles HCl"/(1color(red)(cancel(color(black)("L")))) = (0.1y)color(white)(a)"moles HCl"#
Since you know that the target solution must contain
#0.5x + 0.1y = 0.40" " " "color(orange)((1))#
The target solution has a total volume of
#x + y = 2" " " "color(orange)((2))#
Now simply use equations
#x = 2-y#
#0.5 * (2 -y) + 0.1y = 0.40#
#1 - 0.5y + 0.1y = 0.40#
#-0.4y = -0.60 implies y = ((-0.60))/((-0.4)) = 1.5#
This means that
#x = 2 - 1.5 = 0.5#
So, in order to get
#"0.5 L " -> " 0.5 M HCl solution"#
#"1.5 L " -> " 0.1 M HCl solution"#