Calculating the Volume of Water to be Added
To calculate the volume of water that should be added to the 300ml of 0.5M NaOH solution to achieve a concentration of 10g per ml, we can use the formula:
\[
C_1V_1 + C_2V_2 = C_fV_f
\]
Where:
- \(C_1\) = initial concentration of NaOH (0.5M)
- \(V_1\) = initial volume of NaOH (300ml)
- \(C_2\) = concentration of water (0g/ml)
- \(V_2\) = volume of water to be added
- \(C_f\) = final concentration of the solution (10g/ml)
- \(V_f\) = final volume of the solution

Calculating the Final Volume of the Solution
Given that the final concentration of the solution is 10g/ml, we can rearrange the formula to solve for \(V_f\):
\[
V_f = \frac{C_1V_1 + C_2V_2}{C_f}
\]
Substitute the values into the formula:
\[
V_f = \frac{(0.5M \times 300ml) + (0g/ml \times V_2)}{10g/ml}
\]
\[
V_f = \frac{150 + 0}{10}
\]
\[
V_f = 15ml
\]

Calculating the Volume of Water to be Added
Now that we know the final volume of the solution should be 15ml, we can calculate the volume of water to be added:
\[
V_2 = V_f - V_1
\]
\[
V_2 = 15ml - 300ml
\]
\[
V_2 = -285ml
\]
Since the volume of water cannot be negative, we conclude that no water should be added to the 300ml of 0.5M NaOH solution to achieve a concentration of 10g per ml.