How many milliliters of concentrated hydrochloric acid solution (36.0% HCl by mass, density = 1.18 g/mL) are required to produce 20.0 L of a solution that has a pH of 2.13?
You need to have two pieces of information before applying the dilution formula.
1. You need to convert pH to M.
pH = -log(H^+)
2.13 = pH. I get (H^+) = approximately 0.007 but you need to do that more accurately.
2. You need to convert 36% HCl to molarity.
density = 1.18; therefore, 1000 mL has a mass of 1000 mL x 1.18 g/mL = 1180 grams
That is 36% HCl; thus, 0.36*1180 g = 425 g (approximate)
How many moles is that in the 1000 mL soln? It is 425g/molar mass HCl and that is the molarity.
Then mL x M = mL x M.
11.667
molarity of 36% HCl=11.667
To determine the volume of concentrated hydrochloric acid solution needed, we will use the following steps:
Step 1: Calculate the moles of HCl required.
Step 2: Convert moles to grams.
Step 3: Convert grams to milliliters using density.
Step 1: Calculate the moles of HCl required.
Given that the solution has a pH of 2.13, we know that the concentration of H+ ions is 10^(-pH). Therefore, the concentration of H+ ions in our solution is 10^(-2.13) mol/L.
Since HCl is a strong acid and completely dissociates, the H+ concentration is equal to the HCl concentration.
Now, we can calculate the moles of HCl required. The volume of the solution is given as 20.0 L. Thus, the moles of HCl required can be calculated as:
moles of HCl = (10^(-2.13) mol/L) * (20.0 L) = 0.0072752 mol
Step 2: Convert moles to grams.
To convert moles to grams, we need to know the molar mass of HCl, which is the sum of the atomic masses of hydrogen (H) and chlorine (Cl). The molar mass of HCl is approximately 36.46 g/mol.
mass of HCl = moles of HCl * molar mass of HCl
mass of HCl = 0.0072752 mol * 36.46 g/mol = 0.2652 g
Step 3: Convert grams to milliliters using density.
To convert grams to milliliters, we can use the density of the hydrochloric acid solution. The density is given as 1.18 g/mL.
volume of HCl solution = mass of HCl / density of HCl solution
volume of HCl solution = 0.2652 g / 1.18 g/mL ≈ 0.225 mL
Therefore, approximately 0.225 mL of concentrated hydrochloric acid solution is required to produce 20.0 L of a solution with a pH of 2.13.