A buffer, consisting of H2PO4− and HPO42−, helps control the pH of physiological fluids. Many carbonated soft drinks also use this buffer system. What is the pH of a soft drink in which the major buffer ingredients are 7.20 g of NaH2PO4 and 4.90 g of Na2HPO4 per 355 mL of solution?
To determine the pH of the soft drink, we need to calculate the concentrations of H2PO4− and HPO42− ions in the solution, and then use the Henderson-Hasselbalch equation:
pH = pKa + log([base]/[acid])
where pKa is the dissociation constant of the H2PO4−/HPO42− buffer system.
Step 1: Calculate the moles of NaH2PO4 and Na2HPO4
Given:
Mass of NaH2PO4 = 7.20 g
Molar mass of NaH2PO4 = 119.98 g/mol
Moles of NaH2PO4 = Mass / Molar mass
= 7.20 g / 119.98 g/mol
= 0.06 mol
Given:
Mass of Na2HPO4 = 4.90 g
Molar mass of Na2HPO4 = 141.96 g/mol
Moles of Na2HPO4 = Mass / Molar mass
= 4.90 g / 141.96 g/mol
= 0.03 mol
Step 2: Calculate the concentration of H2PO4− and HPO42−
Since NaH2PO4 is a monobasic acid and Na2HPO4 is a dibasic base, we can assume that one mole of NaH2PO4 will produce one mole of H2PO4− ions and one mole of Na2HPO4 will produce two moles of HPO42− ions.
Concentration of H2PO4− (in mol/L) = moles of H2PO4− / volume of solution (in L)
= 0.06 mol / 0.355 L
= 0.169 mol/L
Concentration of HPO42− (in mol/L) = 2 * moles of HPO42− / volume of solution (in L)
= 2 * 0.03 mol / 0.355 L
= 0.169 mol/L
Step 3: Calculate the pH using the Henderson-Hasselbalch equation
pKa for H2PO4− / HPO42− = 7.21 (at 37°C)
pH = pKa + log([HPO42−]/[H2PO4−])
= 7.21 + log(0.169/0.169)
= 7.21 + log(1)
= 7.21
Therefore, the pH of the soft drink is approximately 7.21.
To determine the pH of the soft drink, we need to understand the acid-base properties of the buffer system and calculate the concentrations of the buffer ingredients.
The buffer system consists of H2PO4− (dihydrogen phosphate ion) and HPO42− (monohydrogen phosphate ion). These ions can react with hydrogen ions (H+) or hydroxide ions (OH-) to maintain a relatively stable pH.
First, we need to calculate the concentrations of H2PO4− and HPO42− in the soft drink solution.
Step 1: Convert the masses of NaH2PO4 and Na2HPO4 to moles.
To do this, we need the molar masses of NaH2PO4 and Na2HPO4:
- NaH2PO4: Na (sodium) = 22.99 g/mol, H2PO4 (dihydrogen phosphate) = 97.99 g/mol >> total molar mass = 120.98 g/mol
- Na2HPO4: Na (sodium) = 22.99 g/mol, HPO4 (monohydrogen phosphate) = 94.97 g/mol >> total molar mass = 156.00 g/mol
Now we can calculate the number of moles of each compound:
- Moles of NaH2PO4 = (mass of NaH2PO4 (g)) / (molar mass of NaH2PO4 (g/mol))
- Moles of Na2HPO4 = (mass of Na2HPO4 (g)) / (molar mass of Na2HPO4 (g/mol))
Step 2: Determine the volume of the solution in liters.
The given volume is 355 mL, which can be converted to liters by dividing by 1000: 355 mL / 1000 = 0.355 L
Step 3: Calculate the concentrations of H2PO4− and HPO42− in moles per liter (Molarity, M).
- Concentration (M) of H2PO4− = (moles of NaH2PO4) / (volume in liters)
- Concentration (M) of HPO42− = (moles of Na2HPO4) / (volume in liters)
Step 4: Construct the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentrations of the acid and its conjugate base:
pH = pKa + log [base] / [acid]
Here, pKa is the equilibrium constant associated with the removal of a proton from the acid, [base] is the concentration of the conjugate base, and [acid] is the concentration of the acid.
Step 5: Determine the pKa value of the H2PO4−/HPO42− buffer system.
The pKa value for the H2PO4−/HPO42− buffer system is 7.21.
Step 6: Use the Henderson-Hasselbalch equation to calculate the pH.
- pH = 7.21 + log [HPO42−] / [H2PO4−]
Substitute the concentrations of H2PO4− and HPO42− in the equation and calculate the value.
By following these steps, you should be able to calculate the pH of the soft drink using the given information.