Problem: How much water should be added to 2M HCl solution to form 1 litre of 0.5M HCl?

Solution:

Step 1: Calculate the number of moles of HCl required for 1 litre of 0.5M HCl solution.

Molarity (M) = Moles of solute / Volume of solution (in litres)

0.5 M = Moles of HCl / 1 L

Moles of HCl = 0.5 mol/L x 1 L = 0.5 mol

Step 2: Use the formula for dilution to calculate the volume of 2M HCl required to make 1 litre of 0.5M HCl solution.

M1V1 = M2V2

Where,

M1 = initial concentration (2M)

V1 = initial volume (unknown)

M2 = final concentration (0.5M)

V2 = final volume (1 L)

Substituting the values in the formula,

2M x V1 = 0.5M x 1 L

V1 = 0.5M / 2M x 1 L

V1 = 0.25 L

Therefore, 0.25 litres of 2M HCl solution is required to make 1 litre of 0.5M HCl solution.

Step 3: Calculate the amount of water required to make up the final volume of 1 litre.

Amount of water = Final volume – Volume of 2M HCl solution

Amount of water = 1 L – 0.25 L

Amount of water = 0.75 L

Therefore, 0.75 litres of water should be added to 0.25 litres of 2M HCl solution to obtain 1 litre of 0.5M HCl solution.

Conclusion: To make 1 litre of 0.5M HCl solution, 0.25 litres of 2M HCl solution should be mixed with 0.75 litres of water.