How many liters of a 3M solution have to be mixed with 2 liters of a 4M solution to yield a 3.6M solution?

We have a 3M solution and a 4M solution and we are supposed to
mix them to create a 3.6M solution. Now if 2 liters of the 4M solution are used, let the volume
of the 3M solution used be equal to L.

The total volume of the final
solution is 2 + L. As we need a 3.6M solution, there should be 3.6*(2 + L) moles in the solutions
we use. The number of moles available in the constituent solutions is 4*2 +
3*L

We now equate 4*2 + 3*L to 3.6*(2 +
L)

=> 4*2 + 3*L = 3.6*(2 +
L)

=> 8 + 3L = 7.2 +
3.6L

=> 8 – 7.2 = 3.6L –
3L

=> .8 = .6L

=> L = .8
/ .6

=> L = 4/3 = 1.33
liters

Therefore the volume of the 3M solution
required is 4/3 liters.