Tris(hydroxymethyl)aminomethane, commonly called TRIS or Trizma, is often used as a buffer in biochemical studies. Its buffering range is pH 7 to 9, and Kb is 1.19 10-6 for the following aqueous reaction.
(HOCH2)3CNH2 + H2O (HOCH2)3CNH3+ + OH -
(HOCH2)3CNH2=TRIS (HOCH2)3CNH3+=TRISH +
What is the pH after 0.59 mL of 12 M HCl is added to a 200.0 mL portion of the buffer?
To find the pH after adding HCl to the buffer, we need to use the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log([A-]/[HA])
Where:
pH is the pH of the buffer solution
pKa is the dissociation constant of the acid component of the buffer
[A-] is the concentration of the conjugate base component of the buffer
[HA] is the concentration of the acid component of the buffer
In this case, the acid component is TRIS (TRIS), and the conjugate base component is TRIS+ (TRISH+).
The pKa of TRIS is not given in the question, so we need to find it. We can calculate the pKa using the Kb (dissociation constant of the conjugate base) provided in the question:
Kb = [TRISH+][OH-]/[TRIS]
Kb = 1.19 x 10^(-6)
Since Kb and Kw (ion product of water) are related, we can use the equation:
Kw = Ka x Kb
Kw = 1.0 x 10^(-14) (at 25°C)
Ka is the dissociation constant for TRIS (acid constant). Since we have Kw and Kb, we can determine Ka:
Ka = Kw / Kb
Ka = 1.0 x 10^(-14) / (1.19 x 10^(-6))
Now that we have obtained Ka, we can calculate pKa:
pKa = -log10(Ka)
Next, we need to calculate the initial concentration of TRIS and TRISH+ in the buffer solution. The volume of the buffer solution is given as 200.0 mL, and the initial concentration of TRIS is not mentioned, so we need to determine it.
To calculate the initial concentration of TRIS, we can use the equation:
C1V1 = C2V2
Where:
C1 is the initial concentration of TRIS
V1 is the initial volume of TRIS (unknown)
C2 is the final concentration of TRIS (12 M)
V2 is the volume of HCl added (0.59 mL)
Solving for V1:
C1V1 = C2V2
C1 x V1 = 12 M x 0.59 mL
V1 = (12 M x 0.59 mL) / C1
The final volume of the buffer solution is 200.0 mL, so the initial volume of TRIS can be calculated as:
Initial volume of TRIS = Final volume of buffer - Volume of HCl added
Initial volume of TRIS = 200.0 mL - 0.59 mL
Now that we have the initial volume of TRIS, we can calculate the initial concentration of TRIS:
Initial concentration of TRIS = C1 = (12 M x 0.59 mL) / Initial volume of TRIS
Now, let's substitute all the values into the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Remember, [A-] refers to the concentration of TRISH+ and [HA] refers to the concentration of TRIS. We now have the pKa value, the initial concentrations of TRIS and TRISH+, and the volumes of TRIS and HCl added.
Simplify the equation using the calculated values and solve for pH.