a) : Molarity of ACES^- (conjugate base)
You start with 3.50 g of sodium ACES salt. The molar mass of ACES^- is 204.1 g/mol as per question text.
Doing the calculation: 3.50 g divided by 204.1 g/mol gives you about 0.01715 moles.
b) : Moles of HCl added
Next, let’s figure out how many moles of HCl you added. You have a concentration of 0.200 M and a volume of 50.0 mL, which is 0.0500 L.
Doing the calculation: 0.200 M times 0.0500 L equals 0.0100 moles.
c) : Reaction between ACES^- and HCl
When ACES^- reacts with HCl, it forms the weak acid HACES, reducing the amount of ACES^- and releasing H^+.
This means the moles of HACES formed equals the moles of HCl added, which is 0.0100 moles. So the moles of ACES^- left are 0.01715 - 0.0100, which is 0.00715 moles.
d) : Final solution concentrations
Now, let's find the concentrations of HACES and ACES^- in the final solution. They are ionizable, and the total volume is 250.0 mL, or 0.250 L.
For HACES, the concentration is 0.0100 moles divided by 0.250 L, which equals 0.0400 M. For ACES⁻, it’s 0.00715 moles divided by 0.250 L, giving you 0.0286 M.
e) : Henderson-Hasselbalch Equation
Now, let's use the Henderson-Hasselbalch equation for HACES and ACES^-. You already know the pKa of ACES is 6.88.
You know: pH = pKa + log([HACES]/[ACES^-]) = 6.88 − 0.146, which is about 6.73.
So, the pH of the buffer solution is 6.73 (rounded to two decimal places).
Bye,
Sandro