Chemistry 120 Question

Question

SOLUTION X IS 10 PERCENT ALCOHOL BY VOLUME, AND SOLUTION Y IS 30 PERCENT ALCOHOL BY

VOLUME. HOW MANY MILLILITERS OF SOLUTION Y MUST BE ADDED TO 200 MILLILITERS OF SOLUTION X

TO CREATE A SOLUTION THAT IS 25 PERCENT ALCOHOL BY VOLUME?

Answer 1

Alligation: (if you've not heard of this, look it up. It is a very useful method)

HAVE..............WANT............NEED.....

10% .......................................5 parts

.........................25%...........................

30%.......................................15 parts

So, you need 5 parts of the 10% and 15 parts of the 30% solution

Since you must use 200 mls of the 10% solution, that makes 5 parts = 200 mls

Thus, 15 parts must = 3 x 200 mls = 600 mls

SUMMARY:

Mix 600 mls of 30% (solution Y) with 200 mls of solution X (10%) to make ~ 800 mls of 25% (assuming volumes are additive)

Check the solution:

600 ml of 30% = 0.30 x 600 = 180 parts alcohol

200 ml of 10% = 0.10 x 200 = 20 parts alcohol

Total parts alcohol = 200

Total volume = 800

Percent alcohol = 200/800 = 0.25 = 25% (as desired)

Using algebra:

(200 ml)(10%) + (y ml)(30%) = (200 ml + y ml)(25%)

2000 + 30y = 5000 + 25y

5y = 3000

y = 600 ml added to 200 ml of x