Sleeping pills often contain barbital, which is weakly acidic (pKa = 8.00). For analysis of the barbital content of a sleeping pill, a titration is carried out with strong base. It takes 12.00 mL of 0.200 M base to reach the stoichiometric point. If the initial acid concentration is 0.0120 M and the solution volume is 200. mL, what is the pH of the solution after adding the following volumes of base solution:4.4ml, 6.0ml.12.0ml, 13.3ml
To determine the pH of the solution after adding different volumes of base solution, we need to calculate the moles of acid and moles of base at each step, and then use that information to find the pH.
Let's begin by calculating the moles of acid initially present in the solution:
Moles of acid = initial acid concentration * solution volume
= 0.0120 M * 200.0 mL
= 0.00240 moles
Next, we can calculate the moles of base added at each step using the volume and concentration of the base solution:
Moles of base = base concentration * base volume
1. For adding 4.4 mL of base solution:
Moles of base = 0.200 M * 0.0044 L
= 0.00088 moles
2. For adding 6.0 mL of base solution:
Moles of base = 0.200 M * 0.0060 L
= 0.0012 moles
3. For adding 12.0 mL of base solution:
Moles of base = 0.200 M * 0.0120 L
= 0.0024 moles
4. For adding 13.3 mL of base solution:
Moles of base = 0.200 M * 0.0133 L
= 0.00266 moles
Now we can determine the moles of acid and base at each step and calculate the resulting concentration of the acid:
Step 1:
Total moles of acid = initial moles of acid - moles of base
= 0.00240 - 0.00088
= 0.00152 moles
Concentration of acid = moles of acid / solution volume
= 0.00152 moles / 200.0 mL
= 0.0076 M
Step 2:
Total moles of acid = initial moles of acid - moles of base
= 0.00240 - 0.0012
= 0.0012 moles
Concentration of acid = moles of acid / solution volume
= 0.0012 moles / 200.0 mL
= 0.006 M
Step 3:
Total moles of acid = initial moles of acid - moles of base
= 0.00240 - 0.0024
= 0 moles
Concentration of acid = moles of acid / solution volume
= 0 moles / 200.0 mL
= 0 M
Step 4:
Total moles of acid = initial moles of acid - moles of base
= 0.00240 - 0.00266
= -0.00026 moles
Concentration of acid = moles of acid / solution volume
= -0.00026 moles / 200.0 mL
= -0.0013 M
Note that in Step 4, the moles of base added are greater than the initial moles of acid, resulting in a negative concentration. This means that the acid has been completely neutralized, and any additional base added will start increasing the pH of the solution.
To find the pH at each step, we can use the equation:
pH = -log10[H+]
where [H+] is the concentration of the acid.
Step 1: pH = -log10(0.0076) ≈ 2.12
Step 2: pH = -log10(0.006) ≈ 2.22
Step 3: The acid has been completely neutralized, so there will be no H+ ions left in solution. Therefore, the pH will be 7 (neutral).
Step 4: Since the concentration of the acid is negative, we need to consider the negative logarithm. pH = -log10(0.0013) ≈ -3.89
To summarize, the pH of the solution after adding the given volumes of base solution is approximately:
4.4 mL: pH ≈ 2.12
6.0 mL: pH ≈ 2.22
12.0 mL: pH = 7 (neutral)
13.3 mL: pH ≈ -3.89