Suppose Compound B is the conjugate base of Compound A. Calculate the approximate concentration of Compound A that must be present in a 0.042 M solution of Compound B to produce a pH of 4.96. The Ka for Compound A is 1.8 x 10^-5 Show your work. Round your final answer to the nearest hundredth decimal place
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To solve this problem, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
where pH is the given pH value (4.96), pKa is the -log(Ka) value (which can be calculated as -log(1.8x10^-5)), [A-] is the concentration of Compound A, and [HA] is the concentration of Compound B (given as 0.042 M).
Let's plug in the known values:
4.96 = (-log(1.8x10^-5)) + log([A-]/0.042)
Rearranging the equation:
(log([A-]/0.042)) = 4.96 - (-log(1.8x10^-5))
(log([A-]/0.042)) = 4.96 + 5log(1.8)
(log([A-]/0.042)) = 4.96 + 5(-log(1.8))
(log([A-]/0.042)) = 4.96 + (-5)(log(1.8))
(log([A-]/0.042)) = 4.96 - 5(log(1.8))
(log([A-]/0.042)) = 4.96 - 0.79588
Taking the inverse logarithm of both sides:
[A-]/0.042 = 10^(4.96 - 0.79588)
[A-]/0.042 = 10^4.16412
[A-] = (10^4.16412)(0.042)
[A-] ≈ 165 M
Therefore, the approximate concentration of Compound A must be 165 M in a 0.042 M solution of Compound B to produce a pH of 4.96.
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