A biochemist makes two solutions with MOPS buffer, solution A contains 0.1 M MOPS and Solution B contains 0.01 M MOPS. The pKa values is 7.5. The pH of both solution is adjust to pH 7.4. In one liter of solution, the proton concentration will be:
A. [H+] of Solution A is 40 nM and [H+] of Solution B is 4 nM
B. [H+] of Solution A is 4 nM and [H+] of Solution B is 40 nM
C. [H+] of Solution A is 40 nM and [H+] of Solution B is 40 nM
D. The [H+] of Solution A and B cannot accurately calculated since the ratio of protonated and deprotonated forms of MOPS is unknown.
I honestly don't know the relationships between acid/base equilibrium and the utilization of Henderson Hasselbalch equation. Please explain this and provide the math.
The Hendrson-Hasselbalch equation is used to find the pH of a buffer system, which is a weak acid and its conjugate base or a weak base and its conjugate acid. The purpose of a buffer is to react with added acid or base to keep the pH stable. The pKa expresses the acid's ability to ionize into H+ ions, so knowing this and the acid and and buffer conccentrations allows you to calculate the pH of the soulution.
In thid problem you're given the pH, which is a direct measure of the concentration of H+ ions. The pH of both solutions is 7.4.
pH = -log[H+], so [H+] = 10^(-pH) = 10^(-7.4) = 4.0 x10^-8 moles per liter
1 nanomole = 10^-9 moles, so the number of nanomoles per liter is:
(4.0x10^-8) x (1nmole/10^-9 moles) = 40. nmole (same for both solutions since they have the same pH)
Answer C is correct.