What mass of solid sodium formate (of MW
68.01)must be added to 125 mL of 0.48 mol/L formic acid (HCOOH) to make a buffer solution having a pH of 4.07? Ka = 0.00018 for HCOOH.
Answer in units of g
To calculate the mass of solid sodium formate needed to make a buffer solution with a pH of 4.07, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Where:
- pH is the desired pH of the buffer solution
- pKa is the logarithm (base 10) of the acid dissociation constant (Ka) of the acid component of the buffer
- [A-] is the concentration of the conjugate base
- [HA] is the concentration of the acid
In this case, the acid is formic acid (HCOOH) and the conjugate base is formate (HCOO-), which is derived from the sodium formate. The acid dissociation constant (Ka) for formic acid is 0.00018.
Step 1: Calculate the pKa
Since we know the Ka value, we can calculate the pKa using the formula: pKa = -log(Ka)
pKa = -log(0.00018) = 3.74
Step 2: Calculate the concentration of the acid ([HA])
The concentration of the acid can be calculated using the formula: [HA] = moles/volume
Given that we have 125 mL of 0.48 mol/L formic acid, let's calculate the number of moles:
[HA] = (0.48 mol/L) x (0.125 L) = 0.06 mol
Step 3: Calculate the concentration of the conjugate base ([A-])
Using the Henderson-Hasselbalch equation, we can rearrange it and solve for [A-]:
[A-] = 10^(pH - pKa) x [HA]
[A-] = 10^(4.07 - 3.74) x 0.06 = 0.081 mol
Step 4: Calculate the mass of sodium formate
Now that we know the concentration of the conjugate base, we can calculate the mass of sodium formate needed:
mass = moles x molecular weight
mass = 0.081 mol x 68.01 g/mol = 5.51 g
Therefore, the mass of solid sodium formate that must be added is 5.51 g.
To calculate the mass of sodium formate needed to make a buffer solution, we need to use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-]/[HA])
In this case, the acid is formic acid (HA), and the conjugate base is formate (A-). By using the given Ka value, we can determine the pKa:
Ka = [A-][H+]/[HA]
0.00018 = [A-] * (10^-4.07) / [HA]
Now, let's look at the balanced equation of the reaction between formic acid (HA) and sodium formate (A-):
HA + A- -> H2O + A-
According to the equation, the ratio of [A-] to [HA] is 1:1. Therefore, we can rewrite the Henderson-Hasselbalch equation using this ratio:
pH = pKa + log (1)
pH = pKa
Substituting the given pH and pKa values into the equation, we can solve for pKa:
4.07 = -log (0.00018)
Now that we have the pKa value, we can determine the ratio of [A-] to [HA]:
[A-]/[HA] = 10^(pH - pKa)
= 10^(4.07 - (-log (0.00018)))
Next, we need to find the moles of formic acid (HA) present in the solution:
Moles of formic acid = concentration (mol/L) * volume (L)
= 0.48 mol/L * 0.125 L
To maintain a 1:1 ratio between [A-] and [HA], we need the same number of moles of sodium formate (A-). The molar mass of sodium formate is 68.01 g/mol:
Mass of sodium formate = moles * molar mass
= 0.48 mol * 68.01 g/mol
Finally, we can calculate the mass of sodium formate needed, rounding to the appropriate number of significant figures:
Mass of sodium formate needed = 0.48 mol * 68.01 g/mol = approximately 32.64 g
Therefore, approximately 32.64 grams of solid sodium formate must be added to 125 mL of 0.48 mol/L formic acid to make a buffer solution with a pH of 4.07.