Question

for a college chemistry experiment, students need to prepare a solution containing ethylene glycol. they are each given 20 fluid ounces of a solution containing 2% ethylene glycol, to which they will add another solution that contains 12% ethylene glycol. how much of the 12% solution should they add to obtain a 5% ethylene glycol solution? write your answer as a whole number or as a decimal rounded to the nearest tenth. fluid ounces

Explanation:

Step1: Calculate initial ethylene glycol amount

The initial 20 - fluid - ounce solution has 2% ethylene glycol. So the amount of ethylene glycol in it is $20\times0.02 = 0.4$ fluid ounces.

Step2: Let the amount of 12% solution be $x$ fluid ounces

The amount of ethylene glycol in the 12% solution is $0.12x$ fluid ounces. The total volume of the final solution is $(20 + x)$ fluid ounces, and the final concentration is 5%. So the amount of ethylene glycol in the final solution is $0.05(20 + x)$ fluid ounces.

Step3: Set up an equation

Based on the conservation of the amount of ethylene glycol, we have the equation $0.4+0.12x=0.05(20 + x)$.

Step4: Expand and solve the equation

Expand the right - hand side: $0.4 + 0.12x=1+0.05x$.
Subtract $0.05x$ from both sides: $0.4 + 0.12x-0.05x=1+0.05x - 0.05x$, which gives $0.4 + 0.07x=1$.
Subtract 0.4 from both sides: $0.07x=1 - 0.4=0.6$.
Divide both sides by 0.07: $x=\frac{0.6}{0.07}\approx8.6$ fluid ounces.

Answer:

8.6