If 2.1 mL of 70.0% alcohol is added to 6.7 mL of water, what is the percent alcohol (%v/v) in the new mixture?

Since we are adding more water to an alcohol solution,

the volume of alcohol in the alcohol will be the same but the volume percent of alcohol will decrease

Initial Volume of Alcohol in the solution:

We are given that 70% of the 2.1 mL solution is alcohol

So, Finding 70% of 2.1

70/100 * 2.1 = 1.470 mL alcohol

Volume of Water in the Solution:

In our initial solution, we have (2.1 - 1.47) mL water

and we add an additional 6.7 mL water in the solution

Hence,

the total amount of water in the solution = (2.1- 1.47) + 6.7

Total amount of water in the solution  = 0.63 + 6.7

Total amount of water in the solution = 7.33 mL

Volume of the final solution = 8.8mL

Percent Alcohol in the new mixture:

Now that we know the volume of alcohol and the volume of water in our mixture, we can now find the percent composition of alcohol

Percent of alcohol (%v/v) = Amount of alcohol / 100mL of solution

Percent of alcohol = (1.47 / 8.8) * 100

Percent of alcohol = 0.167 * 100

Percent of alcohol = 16.7

Therefore, in a 100mL solution, we will have 16.7 mL alcohol