An enzyme-catalyzed reaction is carried out in a 50-mL solution containing 0.1 M TRIS buffer. The pH of the reaction mixture at the start was 8.0. As a result of the reaction, 0.002 mol of H+ were produced. What is the ratio of TRIS base to TRIS acid at the start of the experiment? What is the final pH?
If needed: TRIS(Trizma base) mw= 121.1; pka= 8.3; TRIS-HCl mw= 157.6; pka= 8.3
I kind of have an idea. I start out with the hendersn hasselbalch equation and solve for the ratio ([Tris] / [Tris HCl]). I need help doing this first before i can proceed with the rest of the problem.
Thank you very much.
To solve for the ratio of TRIS base to TRIS acid at the start of the experiment, we can use the Henderson-Hasselbalch equation.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([base]/[acid])
Where:
pH is the pH of the solution
pKa is the acid dissociation constant
[base] is the concentration of the base (TRIS)
[acid] is the concentration of the acid (TRIS-HCl)
In this case, the initial pH of the reaction mixture is 8.0, and the pKa of TRIS is 8.3. We can substitute these values into the equation:
8.0 = 8.3 + log([base]/[acid])
Rearranging the equation, we can solve for [base]/[acid]:
log([base]/[acid]) = 8.0 - 8.3
log([base]/[acid]) = -0.3
Next, we can take the antilog of both sides of the equation to get rid of the logarithm:
[base]/[acid] = 10^(-0.3)
Now, we can calculate the ratio of TRIS base to TRIS acid:
[base]/[acid] = 0.501
So, the ratio of TRIS base to TRIS acid at the start of the experiment is approximately 0.501.
To determine the final pH, we need to consider the produced H+ ions. The reaction produces 0.002 mol of H+ ions.
Since TRIS is a buffer, it can help maintain the pH of the solution by absorbing or releasing H+ ions. Here, the H+ ion is being produced, so the TRIS buffer will act as a base and absorb the H+ ions.
We can calculate the change in concentration of TRIS and TRIS-HCl caused by the production of 0.002 mol of H+ ions. To do this, we can use the molecular weights of TRIS and TRIS-HCl:
Change in concentration of TRIS = (0.002 mol / 50 mL) * (121.1 g/mol) = 0.00484 M
Change in concentration of TRIS-HCl = (0.002 mol / 50 mL) * (157.6 g/mol) = 0.00635 M
Now, we can find the new concentrations of TRIS and TRIS-HCl:
New [TRIS] = [TRIS] initial - change in concentration of TRIS
= 0.1 M - 0.00484 M
= 0.09516 M
New [TRIS-HCl] = [TRIS-HCl] initial - change in concentration of TRIS-HCl
= 0.1 M - 0.00635 M
= 0.09365 M
To find the final pH, we can use the Henderson-Hasselbalch equation again:
pH = pKa + log([base]/[acid])
= 8.3 + log(0.09516/0.09365)
Calculating this, we get:
pH ≈ 8.331
Therefore, the final pH of the reaction mixture is approximately 8.331.