Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 56

A constant electric current flows for \(3.75 \mathrm{~h}\) through two electrolytic cells connected in series. One contains a solution of \(\mathrm{AgNO}_{3}\) and the second a solution of \(\mathrm{CuCl}_{2}\). During this time \(2.00 \mathrm{~g}\) of silver are deposited in the first cell. (a) How many grams of copper are deposited in the second cell? (b) What is the current flowing, in amperes?

Short Answer

Expert verified
(a) To find the mass of copper deposited, calculate the moles of silver and use that to find the moles of copper. Then convert moles of copper to grams. (b) To find the current, calculate the total charge transferred using Faraday’s law of electrolysis and then divide by the total time in seconds.

Step by step solution

01

Find Moles of Silver Deposited

Since we have the mass of silver deposited, we can find the amount in moles. The molar mass of silver (Ag) is approximately 107.87 g/mol. So, the moles of silver deposited are \( \frac{2.00 g}{107.87 g/mol} \).
02

Determine Moles of Copper Deposited

The deposit of silver and copper is a one-electron process, as the reactions are Ag+ + e- → Ag and Cu2+ + 2e- → Cu. So, for every mole of silver deposited, an equivalent amount of copper is deposited. Therefore, the moles of copper deposited are the same as the moles of silver deposited.
03

Calculate Mass of Copper Deposited

Once we have the moles of copper deposited, we can convert it to mass. The molar mass of copper (Cu) is approximately 63.55 g/mol. So, the mass of copper deposited is the product of the moles of copper deposited and the molar mass of copper.
04

Calculate Charge Transferred

Using Faraday’s laws of electrolysis, the total charge Q transferred is given by \(Q = n \cdot F\), where n is the amount of substance in moles and F is the Faraday constant (96485 C/mol). So the total charge transferred is the product of the moles of copper deposited (which is the same as moles of silver) and the Faraday constant.
05

Calculate Current

The electric current I is the charge transferred Q per unit time t (in seconds). Convert 3.75 hours to seconds, then use the formula \(I = \frac{Q}{t}\) to find the current.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

What is a cell diagram? Write the cell diagram for a galvanic cell consisting of an \(\mathrm{Al}\) electrode placed in a \(1 M\) Al(NO \(_{3}\) ) \(_{3}\) solution and a Ag electrode placed in a \(1 M \mathrm{AgNO}_{3}\) solution.

The \(\mathrm{SO}_{2}\) present in air is mainly responsible for the phenomenon of acid rain. The concentration of \(\mathrm{SO}_{2}\) can be determined by titrating against a standard permanganate solution as follows: \(5 \mathrm{SO}_{2}+2 \mathrm{MnO}_{4}^{-}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow \overrightarrow{5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+4 \mathrm{H}^{+}}\) Calculate the number of grams of \(\mathrm{SO}_{2}\) in a sample of air if \(7.37 \mathrm{~mL}\) of \(0.00800 \mathrm{M} \mathrm{KMnO}_{4}\) solution are required for the titration.

A galvanic cell is constructed by immersing a piece of copper wire in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{CuSO}_{4}\) solution and a zinc strip in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{ZnSO}_{4}\) solution. (a) Calculate the emf of the cell at \(25^{\circ} \mathrm{C}\) and predict what would happen if a small amount of concentrated \(\mathrm{NH}_{3}\) solution were added to (i) the \(\mathrm{CuSO}_{4}\) solution and (ii) the \(\mathrm{ZnSO}_{4}\) solution. Assume that the volume in each compartment remains constant at \(25.0 \mathrm{~mL}\). (b) In a separate experiment, \(25.0 \mathrm{~mL}\) of \(3.00 \mathrm{M} \mathrm{NH}_{3}\) are added to the \(\mathrm{CuSO}_{4}\) so- lution. If the emf of the cell is \(0.68 \mathrm{~V},\) calculate the formation constant \(\left(K_{\mathrm{f}}\right)\) of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\)

Write the equations relating \(\Delta G^{\circ}\) and \(K\) to the standard emf of a cell. Define all the terms.

Write the Nernst equation for the following processes at some temperature \(T\). (a) \(\mathrm{Mg}(s)+\mathrm{Sn}^{2+}(a q) \longrightarrow \mathrm{Mg}^{2+}(a q)+\operatorname{Sn}(s)\) (b) \(2 \mathrm{Cr}(s)+3 \mathrm{~Pb}^{2+}(a q) \longrightarrow 2 \mathrm{Cr}^{3+}(a q)+3 \mathrm{~Pb}(s)\)
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation

Nuclear Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Physical Chemistry

Read Explanation

Kinetics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free