To determine the volume of 25 M concentrated sulfuric acid needed to prepare 250 cubic centimeters (cc) of a 2.5 M sulfuric acid solution, we can use the dilution formula:
\[ C_1V_1 = C_2V_2 \]
where:
- \( C_1 \) is the concentration of the concentrated solution (25 M),
- \( V_1 \) is the volume of the concentrated solution we need to find,
- \( C_2 \) is the concentration of the diluted solution (2.5 M),
- \( V_2 \) is the volume of the diluted solution (250 cc or 0.250 L).
First, convert the volume of the diluted solution from cubic centimeters to liters:
\[ V_2 = 250 \text{ cc} = 0.250 \text{ L} \]
Now we can substitute the values into the dilution equation:
\[ (25 , \text{M}) \cdot V_1 = (2.5 , \text{M}) \cdot (0.250 , \text{L}) \]
Calculating the right side:
\[ (2.5 , \text{M}) \cdot (0.250 , \text{L}) = 0.625 , \text{mol} \]
Now we can rearrange the equation to solve for \( V_1 \):
\[ V_1 = \frac{0.625 , \text{mol}}{25 , \text{M}} \]
Calculating \( V_1 \):
\[ V_1 = 0.025 , \text{L} = 25 , \text{mL} \]
Therefore, the volume of 25 M concentrated sulfuric acid solution required to prepare 250 cc of a 2.5 M sulfuric acid solution is 25 mL.