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?
A. 2.70 L
B. 4.54 L
C. 7.18 L
D. 1.05 L

Answer 1

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

\[
C_1V_1 = C_2V_2
\]

where:
- \(C_1\) = concentration of the stock solution = 12.4 M
- \(V_1\) = volume of the stock solution needed (what we are trying to find)
- \(C_2\) = concentration of the diluted solution = 4.4 M
- \(V_2\) = volume of the diluted solution = 7.6 L

Plugging in the values:

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

Calculating the right side:

\[
4.4 \, \text{M} \times 7.6 \, \text{L} = 33.44 \, \text{mol}
\]

Now the equation becomes:

\[
12.4 \, \text{M} \times V_1 = 33.44 \, \text{mol}
\]

Now, solve for \(V_1\):

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

Thus, the volume of stock solution needed is:

\[
\boxed{2.70 \, \text{L}}
\]

So the correct answer is \(A. 2.70 L\).