You prepare a solution from 10.0 mL of 0.100 M MOPS buffer (3-morpholinopropane-1-sulfonic acid) and 10.0 mL of 0.083 M NaOH. Next, you add 1.00 mL of 5.77 × 10-5 M lidocaine to this mixture
Denoting lidocaine as L, calculate the fraction of lidocaine present in the form LH .
To calculate the fraction of lidocaine present in the form LH, we need to determine the pH of the solution first.
1. Calculate the moles of MOPS buffer:
Moles of MOPS = volume (in liters) * concentration
Moles of MOPS = (10.0 mL / 1000 mL/L) * 0.100 M
Moles of MOPS = 0.001 mol
2. Calculate the moles of NaOH:
Moles of NaOH = volume (in liters) * concentration
Moles of NaOH = (10.0 mL / 1000 mL/L) * 0.083 M
Moles of NaOH = 0.00083 mol
3. Determine which component is in excess (MOPS or NaOH):
Since the concentration of NaOH is lower than that of MOPS, NaOH is in excess.
4. Calculate the excess moles of NaOH:
Excess moles of NaOH = moles of NaOH - moles of MOPS
Excess moles of NaOH = 0.00083 mol - 0.001 mol
Excess moles of NaOH = -0.00017 mol (negative because it is in excess)
5. Calculate the total moles of lidocaine:
Total moles of lidocaine = moles of lidocaine added
Total moles of lidocaine = 1.00 mL * (5.77 × 10^-5 M) * (1 L/1000 mL)
Total moles of lidocaine = 5.77 × 10^-8 mol
6. Calculate the moles of lidocaine in the form LH:
Moles of lidocaine in LH = Total moles of lidocaine - excess moles of NaOH
Moles of lidocaine in LH = 5.77 × 10^-8 mol - (-0.00017 mol)
Moles of lidocaine in LH = 1.747 × 10^-4 mol
7. Calculate the total moles of lidocaine:
Total moles of lidocaine = moles of lidocaine in LH + excess moles of NaOH
Total moles of lidocaine = 1.747 × 10^-4 mol + (-0.00017 mol)
Total moles of lidocaine = 1.577 × 10^-4 mol
8. Calculate the fraction of lidocaine in the form LH:
Fraction of lidocaine in LH = (moles of lidocaine in LH) / (total moles of lidocaine)
Fraction of lidocaine in LH = (1.747 × 10^-4 mol) / (1.577 × 10^-4 mol)
Fraction of lidocaine in LH = 1.109
Therefore, the fraction of lidocaine present in the form LH is 1.109.
To calculate the fraction of lidocaine present in the form LH, we need to determine the concentration of LH and the total concentration of lidocaine (LH + L).
First, we need to calculate the final concentrations of MOPS buffer (MOPS) and NaOH in the mixture.
To do this, we can use the equation: C1V1 = C2V2, where C1 and V1 are the initial concentration and volume, and C2 and V2 are the final concentration and volume.
The initial concentration of MOPS buffer is given as 0.100 M, and the volume is 10.0 mL. Thus, C1 = 0.100 M and V1 = 10.0 mL.
The initial concentration of NaOH is given as 0.083 M, and the volume is 10.0 mL. Thus, C1 = 0.083 M and V1 = 10.0 mL.
Using the equation, we can calculate the final concentrations of MOPS buffer and NaOH:
C2 MOPS = (C1 MOPS * V1 MOPS) / V2 Mixture
= (0.100 M * 10.0 mL) / 20.0 mL
= 0.050 M
C2 NaOH = (C1 NaOH * V1 NaOH) / V2 Mixture
= (0.083 M * 10.0 mL) / 20.0 mL
= 0.0415 M
Next, we need to calculate the change in concentration for lidocaine (L) when 1.00 mL of a 5.77 × 10-5 M solution is added.
We can use the same equation: C1V1 = C2V2, where C1 and V1 are the initial concentration and volume, and C2 and V2 are the final concentration and volume.
The initial concentration of lidocaine is given as 5.77 × 10-5 M, and the volume is 1.00 mL. Thus, C1 = 5.77 × 10-5 M and V1 = 1.00 mL.
Using the equation, we can calculate the final concentration of lidocaine:
C2 L = (C1 L * V1 L) / V2 Mixture
= (5.77 × 10-5 M * 1.00 mL) / 20.0 mL
= 2.885 × 10-6 M
Now, to calculate the fraction of lidocaine present in the form LH, we need to compare the concentration of LH to the total concentration of lidocaine (LH + L).
Since the initial concentration of lidocaine (LH) is 0 (as only L is initially present), the fraction of lidocaine present in the form LH is given by the equation:
Fraction of LH = C2 LH / (C2 LH + C2 L)
= 0 / (0 + 2.885 × 10-6 M)
= 0
Therefore, the fraction of lidocaine present in the form LH is 0.