You prepare a solution from 10.0 mL of 0.100 M MOPS buffer (3-morpholinopropane-1-sulfonic acid) and 10.0 mL of 0.071 M NaOH. Next, you add 1.00 mL of 1.89 × 10-5 M lidocaine to this mixture Denoting lidocaine as L, calculate the fraction of lidocaine present in the form LH .
First calculate the pH of the buffer prepared with MOPS and NaOH.
10 mL x 0.1 MOPS acid = 1.0 mmoles.
10 mL x 0.071 = 0.71 mmols NaOH
......MOPSacid + OH^- ==> MOPSbase + H2O
I......1..........0.........0
add.............0.71..........
C......-0.71...-0.71........0.71
E.......0.29......0.........0.71
I have the pKa for MOPS to be 7.20 but use the value in your text/notes.
pH = 7.20 + log(base)/(acid)
I estimate pH = 7.60 or (H^+) = about 2.58E-8
Then Ka for lidocaine I have as about 4E-8 but use the value in your text/notes.
.......HL ==> H^+ + L^-
fraction in HL is alpha zero (Ao).
Ao = (H^+)/[(H^+)+(Ka)]
You know (H^+) from the buffer and you know Ka, solve for Ao.
To calculate the fraction of lidocaine (L) present in the form LH, we need to consider the acid-base equilibrium reaction of lidocaine. In water, lidocaine acts as a weak base.
The equilibrium reaction for lidocaine (L) in water can be represented as follows:
L + H2O ⇌ LH + OH-
From the above reaction, we can see that lidocaine (L) reacts with a water molecule (H2O) to form the protonated form (LH) and hydroxide ion (OH-).
To calculate the fraction of lidocaine present in the form LH, we need to determine the concentrations of L and LH in the solution.
Given:
- Volume of 0.100 M MOPS buffer = 10.0 mL
- Volume of 0.071 M NaOH = 10.0 mL
- Volume of lidocaine solution = 1.00 mL
- Concentration of lidocaine (Lidocaine) = 1.89 × 10-5 M
First, let's calculate the number of moles of L and LH in the solution.
Number of moles of L in lidocaine solution = concentration of lidocaine (Lidocaine) × volume of lidocaine solution
= (1.89 × 10-5 M) × (1.00 mL × 10-3 L/mL)
= 1.89 × 10-8 moles
Now, let's calculate the total volume of the solution.
Total volume of the solution = volume of MOPS buffer + volume of NaOH + volume of lidocaine solution
= 10.0 mL + 10.0 mL + 1.00 mL
= 21.0 mL
The moles of L and LH are related to their respective concentrations by the expression:
moles of species = concentration of species × volume of solution
Using the above expression, the concentration of L in the solution can be calculated as:
Concentration of L = (moles of L)/(total volume of the solution)
= (1.89 × 10-8 moles) / (21.0 mL × 10-3 L/mL)
= 9.0 × 10-7 M
Since we know that the initial concentrations of L and LH are the same (as no reaction has occurred yet), the concentration of LH will also be 9.0 × 10-7 M.
Next, calculate the concentration of OH- ions in the solution. Since the volume of NaOH is 10.0 mL and its concentration is 0.071 M, the moles of OH- ions in the solution can be calculated as:
moles of OH- = concentration of NaOH × volume of NaOH
= (0.071 M) × (10.0 mL × 10-3 L/mL)
= 7.1 × 10-4 moles
Since lidocaine reacts with OH- ions, the concentrations of OH- and LH are directly related. Since the moles of LH is equal to the moles of OH- ions, the concentration of LH will be the same as the concentration of OH- ions, which is 7.1 × 10-4 M.
Now, to calculate the fraction of lidocaine present in the form LH:
Fraction of LH = (concentration of LH) / (concentration of L + concentration of LH)
= (7.1 × 10-4 M) / (9.0 × 10-7 M + 7.1 × 10-4 M)
≈ 0.999224 (rounded to 6 decimal places)
Therefore, the fraction of lidocaine present in the form LH is approximately 0.999224.
To calculate the fraction of lidocaine present in the form LH, we need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of the acid and the ratio of the concentrations of the acid and its conjugate base.
First, let's determine the pH of the solution. We have a buffer solution made from 10.0 mL of 0.100 M MOPS buffer and 10.0 mL of 0.071 M NaOH. The MOPS buffer is a weak acid, so we need to calculate its concentration by multiplying its initial molarity by the volume of the buffer solution:
Concentration of MOPS buffer = (0.100 M) * (10.0 mL) / (20.0 mL) = 0.050 M
Since the NaOH is a strong base, it will completely react with the weak acid MOPS. This means that the concentration of the conjugate base (MOPS-) is equal to the concentration of NaOH:
Concentration of MOPS- = 0.071 M
Next, we need to know the pKa of lidocaine (L). Let's assume the pKa of lidocaine is 7.9.
Now we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this case, LH represents the unionized form of lidocaine (the acid form), and L- represents the ionized form of lidocaine (the conjugate base). So, LH is equivalent to HA in the Henderson-Hasselbalch equation, and L- is equivalent to A-.
We are given the concentration of lidocaine (LH) as 1.89 × 10^-5 M. So, [HA] = 1.89 × 10^-5 M.
And we know the concentration of the conjugate base (L-) is equal to the concentration of the MOPS- buffer, which is 0.071 M. So, [A-] = 0.071 M.
Now, let's substitute these values into the Henderson-Hasselbalch equation and solve for pH:
pH = 7.9 + log(0.071/1.89 × 10^-5)
pH = 7.9 + log(3766.7)
pH ≈ 7.9 + 3.576
pH ≈ 11.476
Since the pH of the solution is 11.476, the fraction of lidocaine present in the form LH can be calculated using the equation:
Fraction of LH = 1 / (1 + 10^(pKa - pH))
Fraction of LH = 1 / (1 + 10^(7.9 - 11.476))
Fraction of LH ≈ 1 / (1 + 10^(-3.576))
Fraction of LH ≈ 1 / (1 + 0.000446)
Fraction of LH ≈ 0.9995
Therefore, the fraction of lidocaine present in the form LH is approximately 0.9995.