How many mL of concentrated HCl (aq) (36.0% HCl by mass, d=1.18 g/mL are required to produce 5.00 L of a solution with a pH =2.10?
You need two bits of information.
a. What is H^+ for pH = 2.10? pH = -log(H^+); solve for (H^+)
b. What is the molarity of the concentrated HCl?
1.18 x 1000 x 0.36 x (1 mol/36.5) = ?M
Mfrom b x mLfrom b = 5.00L x M H^+from a. Solve for mL.
1) find the concentration of H3O+ which is easy since you have the pH
2) find the number of moles of H3O+, remember c=n/v relationship
3) mole ratio! this gives you the number of moles of HCl present, it is a 1:1 ratio remember this from the chemical formula
4) Molarity of HCl this is density times 1000 and then multiply this by 0.36. Finally divide by molar mass of HCl
5) Easiest part yo! just do the c=n/v relationship again to find V since you now know molarity and number of moles
To determine the number of milliliters (mL) of concentrated HCl (hydrochloric acid) needed to produce a 5.00 L solution with a pH of 2.10, we need to follow a step-by-step approach:
Step 1: Calculate the concentration of HCl in the desired solution.
- The concentration of HCl can be determined using the pH value. The pH scale is a logarithmic scale representing the acidity or basicity of a solution. pH is calculated as the negative logarithm of the hydrogen ion concentration ([H+]).
- The equation used to calculate pH is: pH = -log[H+].
- Rearranging the equation, we get: [H+] = 10^(-pH).
- Substituting the given pH value (2.10), we find that [H+] = 10^(-2.10).
- This concentration represents the concentration of H+ ions, which also represents the concentration of HCl in the solution.
Step 2: Calculate the mass of HCl needed to produce the desired solution.
- The desired solution is 5.00 L in volume, and we have determined the concentration of HCl.
- To calculate the mass, we need to use the density of the concentrated HCl solution, which is given as 1.18 g/mL.
- Mass = Volume × Density.
- Mass = 5.00 L × 1.18 g/mL.
Step 3: Calculate the volume of concentrated HCl needed.
- The concentration of HCl is given as a percentage by mass, which means we need to calculate the mass of HCl in the concentrated solution and convert it to volume using its density.
Let's perform the necessary calculations:
Step 1: [H+] = 10^(-2.10) = 0.007943 M (Molarity)
Step 2: Mass = Volume × Density = 5.00 L × 1.18 g/mL = 5.90 g
Step 3: To convert the mass to the volume of concentrated HCl, we need to use the molar mass of HCl, which is approximately 36.46 g/mol.
- First, convert the mass to moles by dividing by the molar mass: Moles = Mass / Molar Mass = 5.90 g / 36.46 g/mol =0.161 moles.
- Use the molarity to convert moles to volume: Volume = Moles / Molarity = 0.161 moles / 0.007943 M = 20.29 L.
Therefore, approximately 20.29 mL of concentrated HCl (36.0% HCl by mass, d=1.18 g/mL) are required to produce 5.00 L of a solution with a pH of 2.10.