The Reaction:
The given reaction is A + B → C + D.

Initial Concentration of Solutions:
- Solution A: 2M
- Solution B: 1.5M

Initial Volumes of Solutions:
- Solution A: 0.5 litre
- Solution B: 2.5 litre

Step 1: Dilution of Solutions:
Both Solution A and Solution B are diluted by 1.5 litres of water.

Final Volumes of Solutions:
- Solution A: 0.5 litre + 1.5 litre = 2 litres
- Solution B: 2.5 litre + 1.5 litre = 4 litres

Final Concentration of Solutions:
- Solution A: 2M (unchanged)
- Solution B: 1.5M (unchanged)

Step 2: Calculation of Moles:
To determine the effect of dilution on the rate of the reaction, we need to calculate the moles of each reactant present in the final solutions.

Moles of Solution A (Initial):
Moles of A = Concentration of A × Volume of A
Moles of A = 2M × 0.5 litres = 1 mole

Moles of Solution B (Initial):
Moles of B = Concentration of B × Volume of B
Moles of B = 1.5M × 2.5 litres = 3.75 moles

Moles of Solution A (Final):
Moles of A = Concentration of A × Volume of A
Moles of A = 2M × 2 litres = 4 moles

Moles of Solution B (Final):
Moles of B = Concentration of B × Volume of B
Moles of B = 1.5M × 4 litres = 6 moles

Step 3: Comparison of Moles:
By comparing the moles of reactants in the initial and final solutions, we can determine the change in the rate of the reaction.

Change in Moles of A:
Initial moles of A = 1 mole
Final moles of A = 4 moles
Change in moles of A = 4 moles - 1 mole = 3 moles

Change in Moles of B:
Initial moles of B = 3.75 moles
Final moles of B = 6 moles
Change in moles of B = 6 moles - 3.75 moles = 2.25 moles

Step 4: Determination of Rate:
The rate of a reaction is directly proportional to the concentration of the reactants. Therefore, the change in the rate of the reaction can be determined by comparing the change in moles of the reactants.

Change in Rate:
Change in rate = (Change in moles of A) / (Change in moles of B)
Change in rate = 3 moles / 2.25 moles = 4/3

Final Explanation:
The rate of the reaction will become 4/3 times the initial rate when