Question

in your chemistry class you have a bottle of 5\% boric acid solution and a bottle of \(2 \%\) boric acid solution. You need 60 milliliters a \(3 \%\) boric acid solution for an experiment. How much of each solution do you need to mix together?

Short answer

The volumes of 5\% and \(2 \%\) boric acid solutions required for preparing the \(3 \%\) boric acid solution will be determined by solving the system of equations

Step-by-step solution

Set up the volume equation

Let x be the volume of 5\% boric acid solution and y be the volume of \(2 \%\) boric acid solution needed. Since the total volume needed is 60 mL, the equation will be: \(x + y = 60\)

Set up the boric acid concentration equation

Since 5\% of the solution x and \(2 \%\) of the solution y should compose \(3 \%\) of the total solution, the equation will be: \(0.05x + 0.02y = 0.03 * 60\)

Solve the system of equations

This system of equations can be solved by substitution or elimination method. In this case, solve the first equation for x: \(x = 60 - y\), and substitute into the second equation to find the value of y: \(0.05(60-y) + 0.02y = 1.8\)

Calculate the volume of each solution

Calculate the value of y and then substitute it back into \(x = 60 - y\) equation to find the value of x. This will provide the volume of each solution needed to prepare a \(3 \%\) boric acid solution