Final answer:
To obtain a 20 oz solution with 22.5% hydrochloric acid, you would need to mix 7.5 oz of 10% hydrochloric acid and 12.5 oz of 30% hydrochloric acid.
Step-by-step explanation:
To find the amounts of 10% and 30% hydrochloric acid needed to obtain a 20 oz solution with 22.5% hydrochloric acid, we can use a mixture equation. Let's represent the amount of 10% acid as x and the amount of 30% acid as 20 - x (since the total solution is 20 oz). Using the equation:
(0.10 * x) + (0.30 * (20 - x)) = 0.225 * 20,
Simplifying the equation gives:
0.10x + 6 - 0.30x = 4.5,
Combining like terms gives:
-0.20x + 6 = 4.5,
Subtracting 6 from both sides gives:
-0.20x = -1.5,
Dividing both sides by -0.20 gives:
x = 7.5.
Therefore, 7.5 oz of the 10% hydrochloric acid and 12.5 oz of the 30% hydrochloric acid should be mixed to obtain a 20 oz solution that is 22.5% hydrochloric acid.