A 1X Phosphate Buffered Saline solution was prepared by adding 1.44g of Na2HPO4 and 1.44g of H2PO4- to 800mL of water. Additional components were dissolved in the solution: 8g of NaCl, 0.2g of KCl and 0.24g KH2PO4. The resulting buffer solution had a pH of 7.2.
a. Calculate the pKa of the buffer.
b. Calculate the pH of the buffer solution after 5.0 mL of 1.0M NaOH.
c. Calculate the pH of the buffer solution after the addition of 5.0 mL 1.0M HCl.
I'm not sure how to incorporate these additional components into my calculations. I got the molarities for everything, but that is as far as I've gotten.
I assume you have solved for the pKa. Here is what you do for the NaOH addition. The addition of HCl is handled the same way. I like to work in millimoles instead of M but you may use your choice.
mmols HPO4^- = (mg/molar mass) = approx 10 but you need a more accurate answer. I will estimate ALLhe following calculations.
mmols H2PO4^- = approx 12
Add NaOH, mmols = approx 5
.......H2PO4^- + OH^- ==> HPO4^2- + H2O
I......12........0.........10
add..............5..............
C......-5.......-5...........5
E......7.........0..........15
Substitute the E line into the HH equation together with your valu for pKa and solve for the new pH of the solution. The HCl addition works the same way but use the base form; i.e
.........HPO4^2- + H^+ ==> H2PO4^-
To answer these questions, you'll need to consider the equilibrium chemistry of the components in the buffer solution. Let's break down the calculations step by step.
Step 1: Calculate the molarities of the different components in the buffer solution.
Given:
- Na2HPO4: 1.44 g
- H2PO4-: 1.44 g
- NaCl: 8 g
- KCl: 0.2 g
- KH2PO4: 0.24 g
- Water volume: 800 mL
First, convert the masses of the compounds to moles using their molar masses. Then, calculate the molarities by dividing the moles by the volume in liters (convert from milliliters).
Molar mass (g/mol):
- Na2HPO4: 141.96 g/mol
- H2PO4-: 97.99 g/mol
- NaCl: 58.44 g/mol
- KCl: 74.55 g/mol
- KH2PO4: 136.09 g/mol
Moles:
- Na2HPO4: (1.44 g / 141.96 g/mol) = 0.01014 mol
- H2PO4-: (1.44 g / 97.99 g/mol) = 0.01468 mol
- NaCl: (8 g / 58.44 g/mol) = 0.137 mol
- KCl: (0.2 g / 74.55 g/mol) = 0.00268 mol
- KH2PO4: (0.24 g / 136.09 g/mol) = 0.00176 mol
Volume of water in liters: (800 mL / 1000) = 0.8 L
Molarities (M):
- Na2HPO4: 0.01014 mol / 0.8 L = 0.012675 M
- H2PO4-: 0.01468 mol / 0.8 L = 0.01835 M
- NaCl: 0.137 mol / 0.8 L = 0.17125 M
- KCl: 0.00268 mol / 0.8 L = 0.00335 M
- KH2PO4: 0.00176 mol / 0.8 L = 0.0022 M
Now that we have the molarities, we can proceed to the calculations.
a. Calculate the pKa of the buffer:
The pKa of a weak acid-component in a buffer can be determined by the Henderson-Hasselbalch equation:
pKa = pH + log10([A-]/[HA])
Here, HA represents the weak acid-component (H2PO4-), and A- represents its corresponding conjugate base (HPO4^2-).
Given: pH = 7.2, [HA] = 0.01835 M, and [A-] = 0.012675 M
pKa = 7.2 + log10(0.012675/0.01835)
b. Calculate the pH of the buffer solution after the addition of 5.0 mL of 1.0 M NaOH:
To calculate the pH after the addition of a strong base, we need to consider the reaction between the base and the acidic component in the buffer (H2PO4-), which results in the formation of its conjugate base (HPO4^2-) and water.
First, calculate the moles of NaOH added:
Moles of NaOH = molarity x volume (L)
Moles of NaOH = 1.0 M x 0.005 L = 0.005 mol
Next, consider the reaction with the acidic component:
H2PO4- + OH- → HPO4^2- + H2O
Using the mole ratio from the balanced equation, we can determine the change in concentrations of each species after the reaction. Since the reactant ratio is 1:1, the moles of NaOH added will be the same as the moles of H2PO4- consumed.
Calculate the new moles of H2PO4-:
Moles of H2PO4- = initial moles - moles of NaOH consumed
Moles of H2PO4- = 0.01468 mol - 0.005 mol
Finally, calculate the new molarity and the resulting pH.
c. Calculate the pH of the buffer solution after the addition of 5.0 mL 1.0 M HCl:
To calculate the pH after the addition of a strong acid, we need to consider the reaction between the acid and the basic component in the buffer (H2PO4-), which results in the formation of its conjugate acid (H3PO4).
This reaction can be represented as follows:
H2PO4- + H+ → H3PO4
Again, using the mole ratio from the balanced equation, we can determine the change in concentrations of each species after the reaction. Since the reactant ratio is 1:1, the moles of HCl added will be the same as the moles of H2PO4- consumed.
Calculate the new moles of H2PO4-:
Moles of H2PO4- = initial moles - moles of HCl consumed
Moles of H2PO4- = 0.01468 mol - (1.0 M x 0.005 L)
Finally, calculate the new molarity and the resulting pH.
Remember to consider the contribution of the additional components (NaCl, KCl, and KH2PO4) to the ionic strength of the solution when calculating pH changes.