Calculate the pH of a solution prepared by mixing 150.mL of 0.174 molal aqueous HF (density=1.10g/mL) with 37.5 g of an aqueous solution that is 1.3% NaOH by mass (density=1.02 g/mL)
To calculate the pH of the solution, we need to determine the concentration of H+ ions in the resulting solution. Here are the steps to find the pH:
Step 1: Calculate the moles of HF.
Given that the volume of HF solution is 150 mL and the molality is 0.174 molal, we can calculate the moles of HF using the following formula:
moles of solute = molality × mass of solvent (in kg) × (1 kg/1000 g)
Since the density of HF solution is given as 1.10 g/mL, the mass of the solvent (HF solution) can be determined by:
mass of solvent = volume of HF solution (in mL) × density of HF solution (in g/mL)
Substituting the given values, we get:
mass of solvent = 150 mL × 1.10 g/mL
Then, convert the mass of solvent to kg:
mass of solvent = 150 mL × 1.10 g/mL × (1 kg/1000 g) = 0.165 kg
Now, we can calculate the moles of HF:
moles of HF = 0.174 molal × 0.165 kg
Step 2: Calculate the moles of NaOH.
Given that the mass of the NaOH solution is 37.5 g and the solution is 1.3% NaOH by mass, we can determine the moles of NaOH using the following formula:
moles of solute = mass of solute (in g) / molar mass of solute
First, calculate the mass of NaOH:
mass of NaOH = 37.5 g × (1% / 100) = 0.375 g
Then, convert the mass of NaOH to moles using the molar mass of NaOH:
molar mass of NaOH = 22.99 g/mol (mass of Na) + 16.00 g/mol (mass of O) + 1.01 g/mol (mass of H)
moles of NaOH = 0.375 g / (22.99 g/mol + 16.00 g/mol + 1.01 g/mol)
Step 3: Calculate the moles of H+ ions.
Since HF is a weak acid, it partially ionizes in water to produce H+ ions. The balanced chemical equation for the ionization of HF is:
HF(aq) ⇌ H+(aq) + F-(aq)
The moles of H+ ions produced will be equal to the moles of HF, which we calculated in Step 1.
moles of H+ ions = moles of HF
Step 4: Calculate the total volume of the resulting solution.
To determine the total volume of the resulting solution, we need to consider the volumes of both the HF and NaOH solutions. We can calculate the volume by dividing the masses of the solutions by their respective densities:
volume = mass of HF solution (in g) / density of HF solution (in g/mL)
+ mass of NaOH solution (in g) / density of NaOH solution (in g/mL)
volume = 150 mL + 37.5 g / 1.02 g/mL
Step 5: Calculate the concentration of H+ ions.
The concentration of H+ ions can be determined by dividing the moles of H+ ions by the total volume of the resulting solution:
[H+] = moles of H+ ions / volume of resulting solution (in L)
Step 6: Calculate the pH.
Finally, we can calculate the pH using the concentration of H+ ions:
pH = -log[H+]
Now, you can plug in the values and perform the calculations to find the pH of the solution.