Answer :
Final answer:
The buffer's pH is approximately 10.3010.
Explanation:
To find the buffer's pH, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Given that pKb1 is 4.00 and pKb2 is 8.00, we can convert them to pKa values using the equation pKa + pKb = 14.00. Therefore, pKa1 = 14.00 - 4.00 = 10.00 and pKa2 = 14.00 - 8.00 = 6.00.
Now, we can substitute the values into the Henderson-Hasselbalch equation:
pH = 10.00 + log([Na2A]/[NaHA])
Since the concentrations of Na2A and NaHA are given as 0.10 mol and 0.050 mol, respectively, in a 1.0 L solution, we can calculate the ratio [Na2A]/[NaHA] as 0.10/0.050 = 2.00.
Substituting this ratio into the equation, we get:
pH = 10.00 + log(2.00)
Using logarithm properties, we can simplify the equation to:
pH = 10.00 + 0.3010
Calculating the sum, we find:
pH = 10.3010
Therefore, the buffer's pH is approximately 10.3010.
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