The problem:
You have a solution with a concentration of 10 moles per liter (decimolar) and a volume of 50 cm3. You need to add water to this solution to convert it to a concentration of 1 mole per liter (centimolar).

The solution:
To solve this problem, you need to calculate the volume of water that must be added to the solution to achieve the desired concentration.

Step 1: Convert the volume of the solution to liters:
The given volume of the solution is 50 cm3. To convert this to liters, divide by 1000 (since 1 liter is equal to 1000 cm3):
50 cm3 ÷ 1000 = 0.05 liters

Step 2: Calculate the number of moles in the initial solution:
Since the concentration of the solution is 10 moles per liter and the volume is 0.05 liters, you can calculate the number of moles using the formula:
Number of moles = Concentration × Volume
Number of moles = 10 mol/L × 0.05 L
Number of moles = 0.5 moles

Step 3: Calculate the final volume of the centimolar solution:
The final concentration of the solution should be 1 mole per liter. Since the number of moles is 0.5, you can calculate the final volume using the formula:
Final volume = Number of moles ÷ Final concentration
Final volume = 0.5 moles ÷ 1 mol/L
Final volume = 0.5 liters

Step 4: Calculate the volume of water to be added:
To calculate the volume of water that needs to be added to the initial solution, subtract the final volume from the initial volume:
Volume of water = Final volume - Initial volume
Volume of water = 0.5 liters - 0.05 liters
Volume of water = 0.45 liters

Step 5: Convert the volume of water to cm3:
To convert the volume of water from liters to cm3, multiply by 1000:
Volume of water = 0.45 liters × 1000
Volume of water = 450 cm3

Therefore, you need to add 450 cm3 of water to the initial 50 cm3 decimolar solution to convert it to a centimolar solution with a concentration of 1 mole per liter.