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?
ask
4.77
To determine the pH of the soft drink, we need to consider the equilibrium between the H2PO4− and HPO42− ions and their respective acid-base reactions.
First, let's calculate the concentration of the buffer components based on their given masses and volume of solution.
The molar mass of NaH2PO4 (sodium dihydrogen phosphate) is:
Na = 22.99 g/mol
H = 1.01 g/mol
P = 30.97 g/mol
O = 16.00 g/mol
Adding these together:
Molar mass of NaH2PO4 = 22.99 + 1.01 + 30.97 + 4(16.00) = 119.98 g/mol
Now, let's calculate the moles of NaH2PO4 from its given mass:
moles of NaH2PO4 = mass / molar mass = 7.20 g / 119.98 g/mol
Next, let's calculate the concentration (in mol/L) of NaH2PO4 in the solution:
concentration of NaH2PO4 (in mol/L) = moles of NaH2PO4 / Volume of solution (in L)
Since the volume of solution is given in mL, we need to convert it to liters:
Volume of solution (in L) = 355 mL / 1000 = 0.355 L
Now, we can substitute the values into the equation:
concentration of NaH2PO4 (in mol/L) = (7.20 g / 119.98 g/mol) / 0.355 L
Repeat the steps above to determine the concentration of Na2HPO4:
Molar mass of Na2HPO4 (disodium phosphate) = 22.99 + 22.99 + 30.97 + 4(16.00) = 141.96 g/mol
moles of Na2HPO4 = 4.90 g / 141.96 g/mol
concentration of Na2HPO4 (in mol/L) = (4.90 g / 141.96 g/mol) / 0.355 L
Now that we have the concentrations of NaH2PO4 and Na2HPO4, we can calculate the pH using the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
The pKa for H2PO4− and HPO42− is 7.21 (at 25 degrees Celsius). The [A-]/[HA] ratio represents the concentration of HPO42− (the conjugate base) over the concentration of H2PO4− (the weak acid).
Substituting the values into the Henderson-Hasselbalch equation:
pH = 7.21 + log([HPO42-] / [H2PO4-])
Now, we need to calculate the [HPO42−] and [H2PO4−] concentrations:
[HPO42-] = concentration of Na2HPO4
[H2PO4-] = concentration of NaH2PO4
Finally, substitute these values into the Henderson-Hasselbalch equation to calculate the pH.
Use the Henderson-Hasselbalch equation.
pH = pKa + log (base)/(acid)
base = Na2HPO4 converted to mols/L
acid = NaH2PO4 converted to moles/L