How do i solve mixtures in word problems?

Question

A photographer wants to mix 2 liters of a 7% acetic acid solution with a 12% solution to get a 9% solution. How many liters of 12% solution must be added?

Answer 1

Adam,

 

Actually this is real life chemistry, not just a word problem! Imagine you have a 7% acidic solution and a 12% acidic solution, but you need 9% for your experiments. If you mix them both the right way, you won't have to buy 9% solution.

 

To do this, calculate the amount of acetic acid and divide it by total volume to achieve 9%.

(2(.07)+.12x)/(2+x)=.09

.14+.12x=.18+.09x

.03x=.04

x=1.333 liters

 

To check our work:

[2*.07+1.333*.12]/(2+1.333)=(.14+.16)/3.333=.09

 

Calculators are notoriously bad at order of operations, so do calculations one at a time and show your work so you don't get the wrong number in the end.

 

Hope that helps!