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Chapter 16: Problem 19

A diprotic acid, \(\mathrm{H}_{2} \mathrm{~A},\) has the following ionization constants: \(K_{a_{1}}=1.1 \times 10^{-3}\) and \(K_{\mathrm{a}_{2}}=2.5 \times 10^{-6} . \mathrm{In}\) order to make up a buffer solution of \(\mathrm{pH} 5.80\), which combination would you choose: NaHA/ \(\mathrm{H}_{2} \mathrm{~A}\) or \(\mathrm{Na}_{2} \mathrm{~A} / \mathrm{NaHA} ?\)

Short Answer

Expert verified
The correct buffer combination to achieve a pH of 5.80 would be NaHA/H2A

Step by step solution

01

Calculate pKa values

To start, one must calculate the pKa values using the given Ka values. Ka is the acid dissociation constant. pKa is simply the negative log of Ka, making it easier to compare acid strengths. For the given values, the formulas would be: pKa1 = -log(Ka1) and pKa2 = -log(Ka2). Plugging Ka1 and Ka2 into those equations results in: pKa1 = -log(1.1 x 10^-3) and pKa2 = -log(2.5 x 10^-6)
02

Calculate the pKa values

By calculating these values, one will find that pKa1 = 2.96 and pKa2 = 5.60.
03

Choose the correct buffer

With calculated pKa values, the selection of the correct buffer is determined by one that matches the desired pH 5.80. With reference to the pH = pKa + log([A-]/[HA]) equation, it would make sense to choose the pair in which pKa and pH values are close to each other. Thus, the pair of species that would make up the buffer would be NaHA and the diprotic acid, H2A. The pKa1 value of 2.96 would be too low to create a buffer of pH 5.80.

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