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Chapter 17: Problem 71

A solution contains \(2.0 \times 10^{-4} \mathrm{MAg}^{+}\) and \(1.5 \times 10^{-3} \mathrm{M}\) \(\mathrm{Pb}^{2+}\). If NaI is added, will AgI \(\left(K_{s p}=8.3 \times 10^{-17}\right)\) or \(\mathrm{PbI}_{2}\) \(\left(K_{s p}=7.9 \times 10^{-9}\right)\) precipitate first? Specify the concentration of \(1^{-}\) needed to begin precipitation.

Short Answer

Expert verified
AgI will precipitate first when NaI is added to the solution. The concentration of I⁻ needed to begin precipitation is \(4.15 \times 10^{-13}\) M.

Step by step solution

01

Calculate the reaction quotient (Q) for each compound.

The reaction quotient, Q, can be calculated using the ion concentrations in solution. For each compound, Q is given by: AgI: \(Q_{1}= \mathrm{[Ag^{+}][I^{-}]} \) PbI₂: \(Q_{2}=\mathrm{[Pb^{2+}][I^{-}]}^2 \) Initially, the I⁻ concentration is 0.
02

Compare the Q values to the Ksp values to determine which compound will precipitate first.

From the given information, we know: Ag⁺ concentration = \(2.0 \times 10^{-4}\) M Pb²⁺ concentration: = \(1.5 × 10^{-3}\) M We will compare the Ksp values for AgI and PbI₂. The lower Ksp indicates the relative ease of precipitation. Ksp for AgI: \(8.3 \times 10^{-17}\) Ksp for PbI₂: \(7.9 \times 10^{-9}\) Since Ksp(AgI) < Ksp(PbI₂), AgI will precipitate first.
03

Calculate the concentration of I⁻ needed for the first compound to precipitate.

Now, we need to find the concentration of I⁻ needed for AgI to precipitate first. To do this, we set Q equal to the Ksp for AgI and solve for the I⁻ concentration: \[Q_{1} = K_{s p} (\mathrm{AgI})\] \[\mathrm{[Ag^{+}][I^{-}]}= 8.3 \times 10^{-17} \] \[\Rightarrow [I^{-}]=\frac{8.3 \times 10^{-17}}{\mathrm{[Ag^{ + }]}}\] \[ [I^{-}]=\frac{8.3 \times 10^{-17}}{2.0 \times 10^{-4}} \] Now, calculating the concentration of I⁻: \[ [I^{-}] = 4.15 \times 10^{-13} \mathrm{M} \] So, the concentration of I⁻ needed to begin precipitation is \(4.15 \times 10^{-13}\) M. AgI will precipitate first when NaI is added to the solution.

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Most popular questions from this chapter

A sample of \(0.1687 \mathrm{~g}\) of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.1150 \mathrm{M} \mathrm{NaOH}\). The acid required \(15.5 \mathrm{~mL}\) of base to reach the equivalence point. (a) What is the molecular weight of the acid? (b) After \(7.25 \mathrm{~mL}\) of base had been added in the titration, the \(\mathrm{pH}\) was found to be 2.85 . What is the \(K_{a}\) for the unknown acid?

A biochemist needs \(750 \mathrm{~mL}\) of an acetic acid-sodium acetate buffer with \(\mathrm{pH}\) 4.50. Solid sodium acetate \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) and glacial acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) are available. Glacial acetic acid is \(99 \% \mathrm{CH}_{3} \mathrm{COOH}\) by mass and has a density of \(1.05 \mathrm{~g} / \mathrm{mL}\). If the buffer is to be \(0.15 \mathrm{M}\) in \(\mathrm{CH}_{3} \mathrm{COOH}\), how many grams of \(\mathrm{CH}_{3} \mathrm{COONa}\) and how many milliliters of glacial acetic acid must be used?

Predict whether the equivalence point of each of the following titrations is below, above, or at \(\mathrm{pH} 7:\) (a) formic acid titrated with \(\mathrm{NaOH},\) (b) calcium hydroxide titrated with perchloric acid, (c) pyridine titrated with nitric acid.

Show that the \(\mathrm{pH}\) at the halfway point of a titration of a weak acid with a strong base (where the volume of added base is half of that needed to reach the equivalence point) is equal to \(\mathrm{p} K_{a}\) for the acid.

Two buffers are prepared by adding an equal number of moles of formic acid (HCOOH) and sodium formate (HCOONa) to enough water to make \(1.00 \mathrm{~L}\) of solution. Buffer \(\mathrm{A}\) is prepared using \(1.00 \mathrm{~mol}\) each of formic acid and sodium formate. Buffer B is prepared by using \(0.010 \mathrm{~mol}\) of each. (a) Calculate the \(\mathrm{pH}\) of each buffer, and explain why they are equal. (b) Which buffer will have the greater buffer capacity? Explain. (c) Calculate the change in \(\mathrm{pH}\) for each buffer upon the addition of \(1.0 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\). (d) Calculate the change in \(\mathrm{pH}\) for each buffer upon the addition of \(10 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\). (e) Discuss your answers for parts (c) and (d) in light of your response to part (b).
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