2. Determine the pH if 0.02 mol of HCl is added to 1.0 L of the buffer described in question #1
question1: 1. How many grams of NaHCO3 should be added to one liter of 0.100 M H2CO3 (Ka = 4.2 x 10-7) to prepare a buffer with pH = 7.00?
1st: equation: H2CO3+HCl<-->H2CO3+Cl
2ndICE For Initial: H2CO3=.42, HCl=.02,H2CO3=..100from?1
For Change:H2CO3=-.02, HCl=-.02,H2CO3=.+.02
For Equilium:H2CO3=.40, HCl=0,H2CO3=.120
2nd:Use Buffer equation: pH= -log(4.2x10-7)+log(.40÷.120)=?
3rd: answer:7pH
Using the Henderson-Hasselblach equation => Salt to Acid Ratio =[NaHCO3]/H2CO3] = 0.238/1. Thus, for a .1M H2CO3 the buffer would be 0.0238M in NaHCO3. => grams of NaHCO3 needed = 0.0238 mole(84 g/mole) = 20 grams.
Adding 0.02mole HCl to the buffer solution => [HCl]added = 0.02M and would shift the equilibrium left.
H2CO3 <=> H^+ + HCO3^-
0.100M - 0.0238M
+0.020M - -0.0200M
0.120M [H^+] 0.0038M
Solve Ka expression for [H^+] = 1.33E-5M => pH = -log(1.33E-5) = 4.88 after adding 0.02 mole HCl into the 1.0 Liter of pH = 7 Buffer.
To determine the pH when 0.02 mol of HCl is added to the buffer described in question #1, we first need to find the initial concentration of the conjugate base and acid in the buffer before adding HCl.
In question #1, we are given the following information:
- The initial concentration of H2CO3 is 0.100 M.
- The Ka value for H2CO3 is 4.2 x 10^(-7).
- The desired pH of the buffer is 7.00.
Step 1: Calculate the initial concentration of the conjugate base (HCO3-) using the Henderson-Hasselbalch equation.
Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
pH = 7.00 (given)
Ka = 4.2 x 10^(-7) (given)
Convert given pH to [H+] concentration:
[H+] = 10^(-pH) = 10^(-7.00) = 1.00 x 10^(-7) M
Plug in the values into the Henderson-Hasselbalch equation:
7.00 = -log(Ka) + log([A-]/[HA])
Rearrange the equation:
log([A-]/[HA]) = 7.00 + log(Ka)
Solve for ([A-]/[HA]):
[A-]/[HA] = 10^(7.00) * 10^(log(Ka))
Converting [A-]/[HA] to a ratio:
[A-]/[HA] = [HCO3-]/[H2CO3] = 10^(7.00) * 10^(log(Ka))
Step 2: Calculate the amount of NaHCO3 to be added to one liter of H2CO3.
Given that the concentration of H2CO3 is 0.100 M, we can calculate the moles of H2CO3 in one liter:
moles of H2CO3 = concentration x volume
moles of H2CO3 = 0.100 M x 1.0 L = 0.100 mol
Since we want to prepare a buffer with a pH of 7.00, the ratio of [HCO3-]/[H2CO3] should be as calculated in step 1:
[HCO3-]/[H2CO3] = 10^(7.00) * 10^(log(Ka))
To maintain this ratio, we need to add an equal molar amount of NaHCO3:
moles of NaHCO3 = moles of H2CO3 = 0.100 mol
Step 3: Convert moles of NaHCO3 to grams using its molar mass.
The molar mass of NaHCO3 is 84.0 g/mol (22.99 g/mol for Na, 1.0 g/mol for H, 12.0 g/mol for C, and 16.0 g/mol for each O).
Mass of NaHCO3 = moles of NaHCO3 x molar mass
Mass of NaHCO3 = 0.100 mol x 84.0 g/mol = 8.4 g
Therefore, 8.4 grams of NaHCO3 should be added to one liter of 0.100 M H2CO3 to prepare a buffer with a pH of 7.00.
Now, going back to the second part of your question, if 0.02 mol of HCl is added to the 1.0 L buffer solution prepared above, we need to consider the reaction between HCl and HCO3-:
HCl + HCO3- → H2CO3 + Cl-
Since HCl is a strong acid, it completely dissociates in water. Therefore, the reaction will consume all the HCO3-, resulting in the formation of more H2CO3 and Cl-.
Since the concentration of H2CO3 has increased and the concentration of HCO3- has decreased, the pH of the buffer solution will decrease. To determine the new pH, we need to calculate the new concentration of [H2CO3].
Given that 0.02 mol of HCl is added to a 1.0 L buffer solution, the new concentration of H2CO3 can be calculated as follows:
New concentration of H2CO3 = (moles of H2CO3 originally in the buffer) + (moles of HCl added)/volume of the solution
New concentration of H2CO3 = (0.100 mol) + (0.02 mol)/(1.0 L)
New concentration of H2CO3 = 0.100 M + 0.02 M
New concentration of H2CO3 = 0.120 M
To determine the new pH of the buffer solution, you would repeat the Henderson-Hasselbalch equation calculation using the new concentration of H2CO3. Substitute the new [H2CO3] value into the equation and solve for pH using the value of pKa (4.2 x 10^(-7)).