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Chapter 18: Problem 71

A baby's spoon with an area of \(6.25 \mathrm{~cm}^{2}\) is plated with silver from \(\mathrm{AgNO}_{3}\) using a current of \(2.00 \mathrm{~A}\) for two hours and 25 minutes. (a) If the current efficiency is \(82.0 \%\), how many grams of silver are plated? (b) What is the thickness of the silver plate formed \(\left(d=10.5 \mathrm{~g} / \mathrm{cm}^{3}\right)\) ?

Short Answer

Expert verified
Answer: The mass of silver plated on the spoon is 15.94 g and the thickness of the silver layer is 0.243 cm.

Step by step solution

01

Calculate the time in seconds

Convert 2 hours and 25 minutes to seconds: 2 hours = 2 * 3600 seconds = 7200 seconds 25 minutes = 25 * 60 seconds = 1500 seconds So, Total time = 7200 + 1500 = 8700 seconds.
02

Calculate the charge passed

To calculate the total charge (Q), we will use the formula: Q = I * t, where I is the current (2 A) and t is the total time in seconds (8700 s). Q = 2.00 A * 8700 s = 17400 C
03

Calculate the charge used for silver plating

To find the charge actually used for silver plating, we need to take into account the current efficiency which is given as 82.0%. Therefore, Charge used for silver plating = 17400 C * 0.820 = 14268 C
04

Find the molar equivalents of silver

There is 1 mole of electron(s) involved in the silver plating process from the electrolysis reaction \(\mathrm{Ag^+ + e^- \rightarrow Ag}\). Using Faraday's constant (F = 96485 C/mol), we can calculate the number of molar equivalents of silver (n) by dividing the used charge (14268 C) by F. n = 14268 C / 96485 C/mol = 0.1478 mol
05

Calculate the mass of silver plated

Now, the mass of silver can be found using the product of the moles of silver and its molar mass (m = n * M). The molar mass of silver (M) is 107.87 g/mol. Mass of silver (m) = 0.1478 mol * 107.87 g/mol = 15.94 g
06

Calculate the volume of the silver plated

To find the volume of silver plated, we will use the formula volume (V) = mass (m) / density (d). The density of silver is given as 10.5 g/cm³. Volume of silver (V) = 15.94 g / 10.5 g/cm³ = 1.518 cm³
07

Calculate the thickness of silver plated

We are given the surface area of the spoon (6.25 cm²). To find the thickness of the silver layer (h), we will use the formula: Volume (V) = Area (A) * Thickness (h). Rearranging the formula, we can find the thickness, h = V / A. So, Thickness of the silver layer (h) = 1.518 cm³ / 6.25 cm² = 0.243 cm. The mass of silver plated on the spoon is 15.94 g and the thickness of the silver layer is 0.243 cm.

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Most popular questions from this chapter

In biological systems, acetate ion is converted to ethyl alcohol in a two- step process: \(\mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+3 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{CH}_{3} \mathrm{CHO}(a q)+\mathrm{H}_{2} \mathrm{O}\) \(E^{o \prime}=-0.581 \mathrm{~V}\) \(\mathrm{CH}_{3} \mathrm{CHO}(a q)+2 \mathrm{H}^{+}(a q)+2 e^{-} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \quad E^{o \prime}=-0.197 \mathrm{~V}\) \(\left(E^{\circ \prime}\right.\) is the standard reduction voltage at \(25^{\circ} \mathrm{C}\) and \(\mathrm{pH}\) of \(7.00 .\) ) (a) Calculate \(\Delta G^{\circ \prime}\) for each step and for the overall conversion. (b) Calculate \(E^{\circ \prime}\) for the overall conversion.

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