Question

A 75.0 mL portion of a 1.60 M solution is diluted to a total volume of 278 mL. A 139 mL portion of that solution is diluted by adding 193 mL of water. What is the final concentration? Assume the volumes are additive.

Answer 1

In this question we have two dilutions occurring, for both cases we will use the dilution formula, which says that the initial concentration and volume of a solution must be equal to the final concentration and volume of the solution, we can better understand that formula presenting it to the question:

M1 * V1 = M2 * V2

where:

M1 = initial molar concentration

V1 = initial volume in liters

M2 = final molar concentration

V2 = final volume in liters

Now let's see what happens in our first dilution:

1.60 M * 0.075 L = M2 * 0.278 L

M2 = 0.43 M, this is the first final concentration

Now we have a solution with 0.43M and 278 mL

In the question we take 139 mL of the 0.43 M solution and add 193 mL, therefore having 332 mL as final volume, let's use the formula again

0.43 M * 0.139 L = M2 * 0.332 L

M2 = 0.180 M as final concentration