Four solutions M, N, O, P of HCl are mixed to produce 100 mL of 0.07 M HCl solution. The molarities of M, N, O and P are 0.05 M, 0.06 M, 0.08 M and 0.09 M respectively. What respec... Four solutions M, N, O, P of HCl are mixed to produce 100 mL of 0.07 M HCl solution. The molarities of M, N, O and P are 0.05 M, 0.06 M, 0.08 M and 0.09 M respectively. What respective volumes of M, N, O and P should be mixed?
Understand the Problem
The question is asking for the respective volumes of four solutions M, N, O, and P that have different molarities. These solutions need to be mixed to create 100 mL of a solution with a specific molarity. The key concepts involved are concentration (molarity), volume, and mixing solutions.
Answer
25 mL, 25 mL, 25 mL, 25 mL
Answer for screen readers
The respective volumes of M, N, O, and P should be: ( 25 , \text{mL}, 25 , \text{mL}, 25 , \text{mL}, 25 , \text{mL} ).
Steps to Solve
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Define the variables and total volume Let ( v_M, v_N, v_O, v_P ) be the volumes in mL of solutions M, N, O, and P respectively. We know that the total volume must equal 100 mL: $$ v_M + v_N + v_O + v_P = 100 $$
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Set up the molarity equation The total amount of HCl in moles contributed by the solutions needs to equal the amount in the final 100 mL of solution at 0.07 M: $$ 0.05 v_M + 0.06 v_N + 0.08 v_O + 0.09 v_P = 0.07 \times 100 $$ Which simplifies to: $$ 0.05 v_M + 0.06 v_N + 0.08 v_O + 0.09 v_P = 7 $$
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Use the provided volume options We will substitute the given options into our equations to see which set satisfies both the volume and molarity requirements.
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Check option A: 25, 25, 25, 25 Calculate:
- Total volume: $$ 25 + 25 + 25 + 25 = 100 \text{ mL} \quad \text{(valid)} $$
- Total moles: $$ 0.05(25) + 0.06(25) + 0.08(25) + 0.09(25) = 1.25 + 1.5 + 2 + 2.25 = 7 \quad \text{(valid)} $$
- Check option B: 50, 25, 12.5, 12.5 Calculate:
- Total volume: $$ 50 + 25 + 12.5 + 12.5 = 100 \text{ mL} \quad \text{(valid)} $$
- Total moles: $$ 0.05(50) + 0.06(25) + 0.08(12.5) + 0.09(12.5) = 2.5 + 1.5 + 1 + 1.125 = 6.125 \quad \text{(not valid)} $$
- Check option C: 25, 50, 10, 15 Calculate:
- Total volume: $$ 25 + 50 + 10 + 15 = 100 \text{ mL} \quad \text{(valid)} $$
- Total moles: $$ 0.05(25) + 0.06(50) + 0.08(10) + 0.09(15) = 1.25 + 3 + 0.8 + 1.35 = 6.4 \quad \text{(not valid)} $$
- Check option D: 50, 25, 15, 10 Calculate:
- Total volume: $$ 50 + 25 + 15 + 10 = 100 \text{ mL} \quad \text{(valid)} $$
- Total moles: $$ 0.05(50) + 0.06(25) + 0.08(15) + 0.09(10) = 2.5 + 1.5 + 1.2 + 0.9 = 6.1 \quad \text{(not valid)} $$
The only option that satisfies both conditions is A.
The respective volumes of M, N, O, and P should be: ( 25 , \text{mL}, 25 , \text{mL}, 25 , \text{mL}, 25 , \text{mL} ).
More Information
This is a classic problem involving the conservation of mass in mixing solutions. Each volume of solution contributes to the overall concentration in the final mixture, reflecting both the volume and concentration of HCl required.
Tips
- Forgetting to check all options thoroughly. It's important to compute both total volume and total moles accurately for each option.
- Misaligning units, leading to incorrect calculations. Ensure all volumes are in mL and concentrations in M.
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