Solutes and Solvents Quick Check

Question

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Question
A stock solution has a concentration of 12.4 M. What volume of stock solution would be needed to make 7.6 L of solution with a concentration of 4.4 M? (1 point)
Responses

2.70 L
2.70 L

1.05 L
1.05 L

7.18 L
7.18 L

4.54 L

Answer 1

To determine the volume of the stock solution needed to create a diluted solution, you can use the dilution equation:

\[ C_1 V_1 = C_2 V_2 \]

Where:

• \( C_1 \) = concentration of the stock solution (12.4 M)
• \( V_1 \) = volume of the stock solution needed
• \( C_2 \) = concentration of the diluted solution (4.4 M)
• \( V_2 \) = volume of the diluted solution (7.6 L)

Rearranging the equation to solve for \( V_1 \):

\[ V_1 = \frac{C_2 V_2}{C_1} \]

Substituting the values into the equation:

\[ V_1 = \frac{(4.4 , \text{M})(7.6 , \text{L})}{12.4 , \text{M}} \]

Calculating:

\[ V_1 = \frac{33.44 , \text{M}\cdot\text{L}}{12.4 , \text{M}} \] \[ V_1 \approx 2.70 , \text{L} \]

Therefore, the correct answer is:

2.70 L