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Chapter 4: Problem 93

Copper metal can reduce silver ions to metallic silver. The copper is oxidized to copper ions according to the reaction $$ 2 \mathrm{Ag}^{+}(a q)+\mathrm{Cu}(s) \longrightarrow \mathrm{Cu}^{2+}(a q)+2 \mathrm{Ag}(s) $$ A copper strip with a mass of \(2.00 \mathrm{~g}\) is dipped into a solution of \(\mathrm{AgNO}_{3}\). After some time has elapsed, the copper strip is coated with silver. The strip is removed from the solution, dried, and weighed. The coated strip has a mass of \(4.18 \mathrm{~g}\). What are the masses of copper and silver metals in the strip? (Hint: Remember that the copper metal is being used up as silver metal forms.)

Short Answer

Expert verified
Answer: The masses of copper and silver in the strip after the reaction are 1.359 g and 2.18 g, respectively.

Step by step solution

01

Calculate the mass gain of silver on the strip

Firstly, we need to find out how much mass the strip has gained after being coated with silver. To do this, subtract the initial mass of the strip (pure copper) from the final mass (copper and silver coated). Mass gain = Final mass - Initial mass Mass gain = 4.18 g - 2.00 g = 2.18 g The strip has gained 2.18 g in mass after being coated with silver.
02

Calculate the amount of silver deposited in moles

Now, find the amount of silver deposited in moles, using the mass gain and molar mass of silver (Ag). Molar mass of Ag = 107.87 g/mol Amount of silver = (Mass gain) / (Molar mass of Ag) Amount of silver = (2.18 g) / (107.87 g/mol) = 0.0202 mol
03

Calculate the moles of copper used

Using the stoichiometry of the reaction, find the amount of copper used in moles. The balanced equation shows that 1 mole of Cu reacts with 2 moles of Ag+. Amount of Cu used = (1/2) × Amount of Ag Amount of Cu used = (1/2) × 0.0202 mol = 0.0101 mol
04

Calculate the mass of copper used in the reaction

Now, calculate the mass of copper used in the reaction using the molar mass of copper (Cu). Molar mass of Cu = 63.55 g/mol Mass of Cu used = Amount of Cu used × Molar mass of Cu Mass of Cu used = 0.0101 mol × 63.55 g/mol = 0.641 g
05

Calculate the remaining mass of copper in the strip

Finally, find the remaining mass of copper in the strip by subtracting the mass of copper used from the initial mass of the strip (pure copper). Mass of remaining Cu = Initial mass of Cu - Mass of Cu used Mass of remaining Cu = 2.00 g - 0.641 g = 1.359 g The remaining mass of copper in the strip is 1.359 g.
06

Determine the masses of copper and silver in the strip

Now, we have found the remaining mass of copper in the strip and the mass of silver that has been coated onto the strip. Mass of Cu in the strip = 1.359 g Mass of Ag in the strip = 2.18 g Thus, the masses of copper and silver in the strip are 1.359 g and 2.18 g, respectively.

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