Determine the pH (to two decimal places) of a solution prepared by adding 15.9 mL of 0.0551 M sodium hydrogen oxalate (NaHOOCCOO) to 0.488 g of sodium oxalate (Na2OOCCOO).
Hydrogen Oxalate pKb of 12.77
Oxalate pKb of 9.81
mmoles acid = 15.9 x 0.0551 = ?
mmoles base = 0.488/molar mass Na2C2O4)
pH = pKa2 + log(base)/(acid)
You must convert pKb above (you want the HC2O4^- to pKa by pKa + pKb = pKw = 14.
Also, I have not taken the volume into account and used ONLY millimoles. Since that is a ratio, mmoles/mmoles cancels out the units AND since concn is mmoles/mL and the mL is the same for acid and base, the volume (whatever it may be) always cancels, too.
To determine the pH of the solution, we need to consider the acid-base properties of the components involved. Sodium hydrogen oxalate (NaHOOCCOO) can act as a weak acid, while sodium oxalate (Na2OOCCOO) is a salt derived from a weak acid and its conjugate base.
First, let's determine the concentrations of the relevant species in the solution.
Step 1: Convert the mass of sodium oxalate to moles
To do this, we need to know the molar mass of sodium oxalate. The molecular formula of sodium oxalate is Na2OOCCOO.
The molar mass of Na2OOCCOO is:
(2*22.99 g/mol) + (2*16.00 g/mol) + (2*12.01 g/mol) = 133.99 g/mol
Given that the mass of sodium oxalate (Na2OOCCOO) is 0.488 g, we can calculate the number of moles:
0.488 g / 133.99 g/mol = 0.003648 mol
Step 2: Calculate the concentration of sodium oxalate (Na2OOCCOO)
We know that the volume of the solution is the sum of the volumes of NaHOOCCOO and Na2OOCCOO:
Volume of solution = Volume of NaHOOCCOO + Volume of Na2OOCCOO
Volume of solution = 15.9 mL + 0 mL = 15.9 mL
Since the density of water is approximately 1 g/mL, the volume of the solution can be used as the volume in liters:
Volume of solution = 15.9 mL = 15.9 mL * (1 L / 1000 mL) = 0.0159 L
The concentration of Na2OOCCOO is then:
Concentration of Na2OOCCOO = moles of Na2OOCCOO / volume of solution
Concentration of Na2OOCCOO = 0.003648 mol / 0.0159 L = 0.2296 M
Now that we know the concentration of Na2OOCCOO, we can determine the concentration of NaHOOCCOO.
Step 3: Determine the concentration of NaHOOCCOO
NaHOOCCOO dissociates into Na+ ions and HOOCCOO- ions, so the concentration of NaHOOCCOO is the same as the concentration of HOOCCOO-.
Since Na2OOCCOO is a salt derived from NaHOOCCOO and its conjugate base, the concentration of NaHOOCCOO is equal to the concentration of HOOCCOO-.
Therefore, the concentration of NaHOOCCOO is also 0.2296 M.
Now, let's use the Henderson-Hasselbalch equation to calculate the pH of the solution.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([base] / [acid])
Given that the pKb of sodium hydrogen oxalate (HOOCCOO-) is 12.77, we can convert it to pKa using the equation:
pKa = 14 - pKb
pKa = 14 - 12.77 = 1.23
Using the Henderson-Hasselbalch equation, substituting the values:
pH = 1.23 + log([HOOCCOO-] / [NaHOOCCOO])
pH = 1.23 + log(0.2296 / 0.2296)
pH = 1.23 + log(1)
pH ≈ 1.23
Therefore, the pH of the solution is approximately 1.23.