Question

A 200 mL of 30% (V/V) of a solution is mixed with 500 mL of 40% (V/V) another solution. What is the volume percentage of resultant solution?

• A. 33.14
• B. 35.00
• C. 26.24
• D. 37.14

Hint:

Weighted Average Formula: $C_{mix} = \frac{C_1V_1 + C_2V_2}{V_1 + V_2}$. Substitute directly: $\frac{30(200) + 40(500)}{700} = \frac{6000 + 20000}{700} = \frac{26000}{700} = 37.14%$.

Answer 1

The Correct Option is D

Step 1: Understanding Volume Percentage (V/V):
Volume percentage is defined as the volume of solute present in 100 mL of solution. \[ % (V/V) = \frac{\text{Volume of solute}}{\text{Total volume of solution}} \times 100 \]
Step 2: Calculate Volume of Solute in each component:
First Solution:

• Total Volume ($V_1$) = 200 mL
• Concentration ($C_1$) = 30%
• Volume of solute ($v_1$) = $\frac{30}{100} \times 200 = 60$ mL

Second Solution:

• Total Volume ($V_2$) = 500 mL
• Concentration ($C_2$) = 40%
• Volume of solute ($v_2$) = $\frac{40}{100} \times 500 = 200$ mL

Step 3: Calculate Resultant Concentration:
Total Volume of solute ($v_{total}$) = $v_1 + v_2 = 60 + 200 = 260$ mL. Total Volume of mixture ($V_{total}$) = $V_1 + V_2 = 200 + 500 = 700$ mL. Resultant Percentage: \[ C_{mix} = \frac{v_{total}}{V_{total}} \times 100 \] \[ C_{mix} = \frac{260}{700} \times 100 \] \[ C_{mix} = \frac{260}{7} \approx 37.1428 \]
Step 4: Final Answer:
The volume percentage is 37.14%.