Question

jill mixes two types of concentrations of hcl (hydrochloric acid): 0.375 liters of 25% hydrochloric acid, and 0.625 liters of 65% hydrochloric acid. what is the hcl concentration of the mixed solution? 50% 40% 56% 44%

Explanation:

Step1: Calculate the amount of HCl in each solution

For the 25% HCl solution: The volume is 0.375 liters, so the amount of HCl is \( 0.375 \times 0.25 = 0.09375 \) liters.
For the 65% HCl solution: The volume is 0.625 liters, so the amount of HCl is \( 0.625 \times 0.65 = 0.40625 \) liters.

Step2: Calculate the total amount of HCl and total volume of the mixed solution

Total HCl amount: \( 0.09375 + 0.40625 = 0.5 \) liters.
Total volume of the mixed solution: \( 0.375 + 0.625 = 1 \) liter.

Step3: Calculate the concentration of the mixed solution

The concentration is \( \frac{0.5}{1} \times 100\% = 50\% \)? Wait, no, wait, let's recalculate. Wait, 0.3750.25 is 0.09375, 0.6250.65: 0.6250.6 = 0.375, 0.6250.05 = 0.03125, so total 0.375+0.03125=0.40625. Then total HCl is 0.09375+0.40625=0.5. Total volume is 1 liter. So concentration is 0.5/1=0.5, so 50%? But wait, maybe I made a mistake. Wait, 0.375 is 3/8, 0.625 is 5/8. So (3/8 0.25) + (5/8 0.65) = (3/8 1/4) + (5/8 13/20) = 3/32 + 65/160 = 15/160 + 65/160 = 80/160 = 0.5, so 50%? Wait, but the options have 50% as an option. Wait, but let me check again. Wait, 0.375 L of 25%: 0.3750.25 = 0.09375 L HCl. 0.625 L of 65%: 0.6250.65 = 0.40625 L HCl. Total HCl: 0.09375 + 0.40625 = 0.5 L. Total volume: 0.375 + 0.625 = 1 L. So concentration is 0.5/1 = 50%. So the answer is 50%.

Wait, but maybe I miscalculated. Wait, 0.375 is 3/8, 0.625 is 5/8. So weighted average: (3/8 25) + (5/8 65) = (75/8) + (325/8) = 400/8 = 50. So 50%. So the correct answer is 50%.

Answer:

50% (Option: 50%)