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Chapter 17: Problem 8

What concentration of ammonia, \(\left[\mathrm{NH}_{3}\right],\) should be present in a solution with \(\left[\mathrm{NH}_{4}^{+}\right]=0.732 \mathrm{M}\) to produce a buffer solution with \(\mathrm{pH}=9.12 ?\) For \(\mathrm{NH}_{3}\) \(K_{\mathrm{h}}=1.8 \times 10^{-5}\)

Short Answer

Expert verified
The concentration of ammonia in the solution should be 240.45 M.

Step by step solution

01

Understand the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is: \( pH = pK_a + log \left(\frac{[Base]}{[Acid]}\right)\) Here, we'll modify this a bit for the given exercise where \(K_h = [H_3O^+][NH_3]/[NH_4^+]\). Taking negative logarithm on both sides we get \(pH = pK_a + log \left(\frac{[NH_3]}{[NH_4^+]}\right)\)
02

Calculate the \(pK_a\)

The \(pK_a\) is calculated from the \(K_h\) by taking the negative logarithm of \(K_h\): \(pK_a = -log(K_h)\); given \(K_h = 1.8 \times 10^{-5}\), hence \(pK_a = -log(1.8 \times 10^{-5}) = 4.74\)
03

Solve the Henderson Hasselbalch equation for the concentration of ammonia

Now that we have \(pH\), \(pK_a\) and \([NH_4^+]\), we can solve for \([NH_3]\) in the Henderson-Hasselbalch equation: \(9.12 = 4.74 + log \left(\frac{[NH_3]}{0.732}\right)\); Solving this gives the ammonia concentration: \([NH_3] = 0.732 \times 10^{(9.12 - 4.74)} = 0.732 \times 10^{4.38} = 240.45 \,M \)

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Most popular questions from this chapter

Indicate which of the following aqueous solutions are buffer solutions, and explain your reasoning. (a) \(0.100 \mathrm{M} \mathrm{NaCl}\) (b) \(0.100 \mathrm{M} \mathrm{NaCl}-0.100 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) (c) \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{2}-0.150 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\) (d) \(0.100 \mathrm{M} \mathrm{HCl}-0.050 \mathrm{M} \mathrm{NaNO}_{2}\) (e) \(0.100 \mathrm{M} \mathrm{HCl}-0.200 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{COO}\) (f) \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}-0.125 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{COO}\)

You are asked to prepare a \(\mathrm{KH}_{2} \mathrm{PO}_{4}-\mathrm{Na}_{2} \mathrm{HPO}_{4}\) solu- tion that has the same \(\mathrm{pH}\) as human blood, 7.40 (a) What should be the ratio of concentrations \(\left[\mathrm{HPO}_{4}^{2-}\right] /\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right]\) in this solution? (b) Suppose you have to prepare \(1.00 \mathrm{L}\) of the solution described in part (a) and that this solution must be isotonic with blood (have the same osmotic pressure as blood). What masses of \(\mathrm{KH}_{2} \mathrm{PO}_{4}\) and of \(\mathrm{Na}_{2} \mathrm{HPO}_{4} \cdot 12 \mathrm{H}_{2} \mathrm{O}\) would you use? [Hint: Refer to the definition of isotonic on page \(580 .\) Recall that a solution of \(\mathrm{NaCl}\) with \(9.2 \mathrm{g} \mathrm{NaCl} / \mathrm{L}\) solution is isotonic with blood, and assume that \(\mathrm{NaCl}\) is completely ionized in aqueous solution.]

Briefly describe each of the following ideas, phenomena, or methods: (a) the common-ion effect; (b) the use of a buffer solution to maintain a constant \(\mathrm{pH}\) (c) the determination of \(\mathrm{p} K_{\mathrm{a}}\) of a weak acid from a titration curve; (d) the measurement of \(\mathrm{pH}\) with an acid-base indicator.

This single equilibrium equation applies to different phenomena described in this or the preceding chapter. \(\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{CH}_{3} \mathrm{COO}^{-}\) Of these four phenomena, ionization of pure acid, common-ion effect, buffer solution, and hydrolysis, indicate which occurs if (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) are high, but \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is very low. (b) \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is high, but \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) are very low. (c) \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) is high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are low. (d) \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is low.

You are asked to bring the \(\mathrm{pH}\) of \(0.500 \mathrm{L}\) of \(0.500 \mathrm{M}\) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq})\) to 7.00 How many drops \((1 \text { drop }=0.05 \mathrm{mL})\) of which of the following solutions would you use: \(10.0 \mathrm{M} \mathrm{HCl}\) or \(10.0 \mathrm{M} \mathrm{NH}_{3} ?\)
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