A 1.00 L volume of buffer is made with concentrations of 0.350 M NaCHO2 and .550 M HCHO2. a) What is the initial pH of the buffer? b) What is the pH after the addition of .0050 mol HCL? c) What is the pH after the addition of .0050 mols NaOH?
Use the Henderson-Hasselbalch equation.
To answer these questions, we need to understand the concept of a buffer and its response to acid or base addition.
A buffer is a solution that resists changes in pH when either an acid or a base is added to it. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, the buffer is made of sodium formate (NaCHO2) and formic acid (HCHO2).
a) To find the initial pH of the buffer, we need to calculate the pH using the Henderson-Hasselbalch equation:
pH = pKa + log([conjugate base]/[weak acid])
In this case, formic acid (HCHO2) is a weak acid, and we know the concentration of the weak acid ([HCHO2]) and its conjugate base ([NaCHO2]). We also need to know the pKa value for formic acid.
b) To find the pH after the addition of HCl (hydrochloric acid), we need to consider the reaction that takes place between HCl and the components of the buffer. The HCl will react with the formate ion (NaCHO2) in the buffer to form formic acid (HCHO2). We need to calculate the resulting concentrations of formic acid and its conjugate base and then use the Henderson-Hasselbalch equation to find the pH.
c) To find the pH after the addition of NaOH (sodium hydroxide), we need to consider the reaction that takes place between NaOH and the components of the buffer. The NaOH will react with the formic acid (HCHO2) in the buffer to form the formate ion (NaCHO2). We need to calculate the resulting concentrations of formic acid and its conjugate base and then use the Henderson-Hasselbalch equation to find the pH.
Now, let's calculate the answers to each part of the question:
a) To find the initial pH of the buffer, we need to use the Henderson-Hasselbalch equation. The pKa value for formic acid (HCHO2) is usually given in the question or can be found in a reference source. Let's assume the pKa of formic acid is 3.75.
pH = 3.75 + log([NaCHO2]/[HCHO2])
= 3.75 + log(0.550/0.350)
= 3.75 + log(1.5714)
= 3.75 + 0.1960
≈ 3.95
Therefore, the initial pH of the buffer is approximately 3.95.
b) To find the pH after the addition of 0.0050 mol of HCl, we need to calculate the new concentrations of formic acid and its conjugate base. We know that HCl reacts with NaCHO2 to form HCHO2:
HCl + NaCHO2 -> HCHO2 + NaCl
Since we have 0.0050 mol of HCl and an equal stoichiometric ratio between HCl and NaCHO2, the entire 0.0050 mol of NaCHO2 will react. Therefore, the concentration of NaCHO2 is reduced to zero, while the concentration of HCHO2 increases by 0.0050 mol.
Using the Henderson-Hasselbalch equation with these new concentrations:
pH = 3.75 + log([0]/[0.350 - 0.0050])
= 3.75 + log(0/0.3450)
= 3.75 + log(0)
= undefined (since log(0) is undefined)
Therefore, the pH after the addition of 0.0050 mol of HCl is undefined because all of the NaCHO2 has reacted.
c) To find the pH after the addition of 0.0050 mol of NaOH, we need to calculate the new concentrations of formic acid and its conjugate base. We know that NaOH reacts with HCHO2 to form NaCHO2:
NaOH + HCHO2 -> NaCHO2 + H2O
Since we have 0.0050 mol of NaOH and an equal stoichiometric ratio between NaOH and HCHO2, the entire 0.0050 mol of HCHO2 will react. Therefore, the concentration of HCHO2 is reduced to zero, while the concentration of NaCHO2 increases by 0.0050 mol.
Using the Henderson-Hasselbalch equation with these new concentrations:
pH = 3.75 + log([0.0050]/[0 - 0.0050])
= 3.75 + log(0.0050/-0.0050)
= 3.75 + log(-1)
= undefined (since log(-1) is undefined)
Therefore, the pH after the addition of 0.0050 mol of NaOH is undefined because all of the HCHO2 has reacted.
In summary, the initial pH of the buffer is approximately 3.95. After the addition of 0.0050 mol of HCl or NaOH, the pH becomes undefined because all of the NaCHO2 or HCHO2 has reacted.