To find the volume of stock solution needed, 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 (unknown)
- \( C_2 \) = concentration of the diluted solution (4.4 M)
- \( V_2 \) = volume of the diluted solution (7.6 L)
Plugging in the known values:
\[ 12.4 , \text{M} \times V_1 = 4.4 , \text{M} \times 7.6 , \text{L} \]
Calculating the right side:
\[ 4.4 \times 7.6 = 33.44 \]
So the equation becomes:
\[ 12.4 , V_1 = 33.44 \]
Now, solve for \( V_1 \):
\[ V_1 = \frac{33.44}{12.4} \]
Calculating \( V_1 \):
\[ V_1 \approx 2.70 , \text{L} \]
So, the volume of the stock solution needed is 2.70 L.