How many liters of pure acid should be added to 25 liters of a 60% solution of acid to obtain a 75% acid solution?

Question

Wyatt Atkins · Accepted Answer

You need to add 15 L of pure acid.

The idea behind this problem is that you are adding pure acid to a solution that already has 60% v/v acid. As a result, the added acid will increase the volume of both the solvent and the solute by the same amount, changing the starting solution's percent concentration. Therefore, measure the amount of acid in your starting solution first. #25color(red)(cancel(color(black)("L solution"))) * "60 L acid"/(100color(red)(cancel(color(black)("L solution")))) = "15 L acid"# Let's say that #x# denotes the volume of pure acid that you must add to your starting solution. Since you're dealing with pure acid, the volume of acid will Increase by #x# #V_"acid" = 15 + x# At the same time, the volume of the solution will also incrase by #x# #V_"sol" = 25 + x# This indicates that the percent concentration by volume of the target solution will be equal to #V_"acid"/V_"soL" * 100 = 75%# #((15 + x)color(red)(cancel(color(black)("L"))))/((25 + x)color(red)(cancel(color(black)("L")))) * 100 = 75%# Solve this equation for #x# to get #(15+x) * 100 = (25 + x) * 75# #1500 + 100x = 1875 + 75x# #25x = 375 implies x = 375/25 = color(green)("15 L")# Thus, you will obtain 40 L of 75% v/v acid solution if you add 15 L of pure acid to 25 L of 60% v/v acid solution.

Cameron Andrews · Answer

undefined To obtain a 75% acid solution, add 25 liters of pure acid to the 25 liters of the 60% solution.