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Chapter 18: Problem 35

When \(200.0 \mathrm{mL}\) of \(0.350 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}(\mathrm{aq})\) are added to 200.0 mL of 0.0100 M AgNO 3(aq), what percentage of the \(\mathrm{Ag}^{+}\) is left unprecipitated?

Short Answer

Expert verified
The percentage of unprecipitated \(Ag^{+}\) is 0%.

Step by step solution

01

Identify the reaction

The first step is identifying the reaction. When \(AgNO_3\) and \(K_2CrO_4\) are mixed, they react to form \(Ag_2CrO_4\) and \(KNO_3\), with the \(Ag_2CrO_4\) precipitating out. The balanced chemical equation for this reaction is: \[2AgNO_3(aq) + K_2CrO_4(aq) \rightarrow Ag_2CrO_4(s) + 2KNO_3(aq)\]
02

Method to Calculate the Remaining Ag+

Calculate the initial number of moles of \(\mathrm{Ag}^{+}\) and \(K_2CrO_4\) respectively. The formula to calculate moles is given by \(Molarity = moles/volume\). Hence moles = Molarity x Volume. \[Moles_{Ag^{+}}= 0.0100 \, Molarity \times 200.0 \, mL = 0.002 \, moles\] \[Moles_{K_2CrO_4}= 0.350 \, Molarity \times 200.0 \, mL = 0.0700 \, moles\] Next, find out how much \(Ag^{+}\) will get precipitated out by \(K_2CrO_4\). From the equation, we can see that 1 mol of \(K_2CrO_4\) reacts with 2 mol of \(Ag^+\). So, \(0.0700 \, mol of \, K_2CrO_4\) should react with \(2 \times 0.0700 = 0.0140 \, mol of \, Ag^+\).
03

Calculate percentage of unreacted Ag+

Calculate the remaining \(Ag^{+}\) by subtracting reacted \(Ag^{+}\) from initial \(Ag^{+}\). \[Remaining \, Ag^{+} = Initial \, Ag^{+} - Reacted \, Ag^{+} = 0.002 \, mol - 0.0140 \, mol = -0.012 \, mol\] Since the \(Remaining \, Ag^{+}\) is negative, it means that all \(Ag^{+}\) has reacted and none remained unreacted thus leading to no unprecipitated \(Ag^{+}\). So, the percentage of unprecipitated \(Ag^{+}\) is 0%.

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Most popular questions from this chapter

To increase the molar solubility of \(\mathrm{CaCO}_{3}(\mathrm{s})\) in a saturated aqueous solution, add (a) ammonium chloride; (b) sodium carbonate; (c) ammonia; (d) more water.

Which of the following saturated aqueous solutions would have the highest \(\left[\mathrm{Mg}^{2+}\right]\): (a) \(\mathrm{MgCO}_{3} ;\) (b) \(\mathrm{MgF}_{2};\) (c) \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2} ?\) Explain.

Calculate \(\left[\mathrm{Cu}^{2+}\right]\) in a \(0.10 \mathrm{M} \mathrm{CuSO}_{4}(\) aq) solution that is also \(6.0 \mathrm{M}\) in free \(\mathrm{NH}_{3}\). \(\mathrm{Cu}^{2+}(\mathrm{aq})+4 \mathrm{NH}_{3}(\mathrm{aq}) \rightleftharpoons\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}(\mathrm{aq})\) \(K_{\mathrm{f}}=1.1 \times 10^{13}\)

Calculate the aqueous solubility, in moles per liter, of each of the following. (a) \(\mathrm{BaCrO}_{4}, K_{\mathrm{sp}}=1.2 \times 10^{-10}\) (b) \(\mathrm{PbBr}_{2}, K_{\mathrm{sp}}=4.0 \times 10^{-5}\) (c) \(\mathrm{CeF}_{3}, K_{\mathrm{sp}}=8 \times 10^{-16}\) (d) \(\operatorname{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}, K_{\mathrm{sp}}=2.1 \times 10^{-20}\)

Without performing detailed calculations, indicate whether either of the following compounds is appreciably soluble in \(\mathrm{NH}_{3}(\mathrm{aq}):(\mathrm{a}) \mathrm{CuS}, K_{\mathrm{sp}}=6.3 \times 10^{-36},\)(b) \(\mathrm{CuCO}_{3}, K_{\mathrm{sp}}=1.4 \times 10^{-10} .\) Also use the fact that \(K_{\mathrm{f}}\) for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is \(1.1 \times 10^{13}\).
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