To determine the volume of concentrated HCl needed, we start by understanding the relationship between pH and hydrogen ion concentration. A solution with a pH of 2.00 has a hydrogen ion concentration of:
[H+] = 10-pH = 10-2 = 0.01 M
Since we want to prepare 500 ml of this solution, we can find the total moles of H+ needed:
Total moles = Concentration × Volume = 0.01 mol/L × 0.5 L = 0.005 moles
Now, we need to find how much of concentrated HCl is required to supply these 0.005 moles of H+. Concentrated HCl is 37% HCl by mass, which means for every 100 g of solution, there are 37 g of HCl. The molar mass of HCl is approximately 36.46 g/mol, so we can calculate the number of moles in 37 g of HCl:
moles of HCl = mass ÷ molar mass = 37 g ÷ 36.46 g/mol ≈ 1.01 moles
This means that in 100 g of concentrated HCl solution, there are about 1.01 moles of HCl. We can calculate the amount of solution to dilute by using the concentration:
Concentration of concentrated HCl = 1.01 moles / 0.1 L = 10.1 M
Now, we can find the volume of concentrated HCl required to get 0.005 moles:
Volume = moles / concentration = 0.005 moles / 10.1 M ≈ 0.000495 m³ = 0.495 L = 495 ml
Since this amount exceeds the total volume we want (500 ml), we need to dilute appropriately. Instead, let’s calculate it based on the volume we can actually measure:
We need to dilute a specific volume of concentrated HCl solution that will give us the required 0.005 moles when mixed with water to total 500 ml. Using the dilution equation (C1V1 = C2V2) to find this:
– Let C1 = 10.1 M (concentration of concentrated HCl)
– C2 = 0.01 M (desired concentration)
– V2 = 500 ml
Now substituting into the equation:
10.1 M × V1 = 0.01 M × 500 ml
V1 = (0.01 M × 500 ml) / 10.1 M
V1 ≈ 0.0495 L = 49.5 ml
Therefore, to prepare 500 ml of a solution with a pH of 2.00, you should dilute approximately 49.5 ml of concentrated HCl with water to reach the desired total volume.