To calculate the molarity of the concentrated hydrochloric acid solution and the volume required to make a 0.10 M HCl solution, you can use the following steps:
(i) Calculate the molarity of the concentrated HCl solution:
Molarity (M) is defined as the number of moles of solute (in this case, HCl) per liter of solution. First, we need to find the number of moles of HCl in 100 g of the concentrated solution.
Given:
Mass of HCl in the solution = 38% of 100 g = 0.38 × 100 g = 38 g
Molar mass of HCl (HCl has one hydrogen atom and one chlorine atom):
Hydrogen (H) = 1 g/mol
Chlorine (Cl) = 35.5 g/mol
Molar mass of HCl = 1 g/mol + 35.5 g/mol = 36.5 g/mol
Now, calculate the number of moles of HCl:
Number of moles of HCl = Mass of HCl (g) / Molar mass of HCl (g/mol)
Number of moles of HCl = 38 g / 36.5 g/mol ≈ 1.04 moles
Now, you want to find the molarity of the solution. You are given the density of the solution, which is 1.19 g/L. This means that 1 liter of the solution has a mass of 1.19 grams.
Molarity (M) = Number of moles of solute / Volume of solution (in liters)
Molarity (M) = 1.04 moles / (1.19 L) ≈ 0.874 M
So, the molarity of the concentrated hydrochloric acid solution is approximately 0.874 M.
(ii) Calculate the volume of concentrated HCl required to make 1.0 L of a 0.10 M HCl solution using the dilution formula:
C1V1 = C2V2
Where:
C1 = Initial concentration (Molarity) of the concentrated HCl solution
V1 = Volume of the concentrated HCl solution needed
C2 = Desired concentration (Molarity) of the diluted HCl solution
V2 = Final volume of the diluted HCl solution
Given:
C1 = 0.874 M (from part i)
C2 = 0.10 M
V2 = 1.0 L (since you want to make 1.0 L of the diluted solution)
Now, solve for V1:
0.874 M * V1 = 0.10 M * 1.0 L
V1 = (0.10 M * 1.0 L) / 0.874 M
V1 ≈ 0.114 L
So, you would need approximately 0.114 liters (or 114 mL) of the concentrated hydrochloric acid solution to make 1.0 liter of a 0.10 M HCl solution.
