Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 94

Elemental calcium is produced by the electrolysis of molten \(\mathrm{CaCl}_{2}\). (a) What mass of calcium can be produced by this process if a current of \(7.5 \times 10^{3} \mathrm{~A}\) is applied for $48 \mathrm{~h}\( ? Assume that the electrolytic cell is \)68 \%$ efficient. (b) What is the minimum voltage needed to cause the electrolysis?

Short Answer

Expert verified
The mass of calcium produced by the electrolysis of molten \(\mathrm{CaCl}_{2}\) with a current of \(7.5 \times 10^{3}\) A applied for \(48\) hours and a cell efficiency of \(68\%\) is approximately \(7.67 \times 10^{4}\) g. The minimum voltage needed to cause electrolysis is equal to the standard reduction potential of calcium, which is \(-2.87\) V.

Step by step solution

01

(Step 1: Calculate the total charge passed through the electrolyte)

Use the formula: charge = current × time. The total charge, \(Q\), passed through the electrolytic cell is given by: $$ Q = I \cdot t $$ Where \(I = 7.5 \times 10^{3} A\) is the current and \(t = 48 h\) is the time. We will convert the time to seconds so that the units are consistent: $$ t = 48 h \cdot \frac{3600 s}{1 h} $$ Hence, calculate the total charge \(Q\).
02

(Step 2: Calculate the number of moles of electrons passed)

To find the number of moles of electrons we can use Faraday's constant, \(F = 96,485~C/mol\): $$ n(\text{electrons}) = \frac{Q}{F} $$ Calculate the number of moles of electrons by dividing the total charge \(Q\) obtained in Step 1 by Faraday's constant.
03

(Step 3: Find the number of moles of Calcium produced)

In the electrolysis process, calcium is produced from its ion, \(\mathrm{Ca}^{2+}\). The balanced half-reaction for the process is: $$ \mathrm{Ca}^{2+} + 2e^{-} \rightarrow \mathrm{Ca (s)} $$ This reaction implies that for every 2 moles of electrons, 1 mole of calcium is produced. Therefore, we can calculate the number of moles of calcium produced as: $$ n(\text{Ca}) = \frac{1}{2} n(\text{electrons}) $$ Calculate the number of moles of calcium produced using the number of moles of electrons obtained in Step 2.
04

(Step 4: Consider cell efficiency and calculate the actual moles of Calcium produced)

The problem states that the efficiency of the electrolytic cell is \(68\%\). To find the actual moles of calcium produced, multiply the number of moles of calcium obtained in Step 3 by the cell efficiency: $$ n_{\text{actual}}(\text{Ca}) = 0.68 \cdot n(\text{Ca}) $$
05

(Step 5: Calculate the mass of Calcium produced)

The mass of calcium produced can be calculated using the molar mass of calcium (\(M_{\text{Ca}} = 40.08 g/mol\)): $$ m_{\text{actual}}(\text{Ca}) = n_{\text{actual}}(\text{Ca}) \times M_{\text{Ca}} $$ Calculate the actual mass of calcium produced.
06

(Step 6: Identify the reduction potential for Calcium)

To answer part (b) of the exercise, we need to determine the minimum voltage needed for the electrolysis. Consider the reduction half-reaction for calcium: $$ \mathrm{Ca}^{2+} + 2e^{-} \rightarrow \mathrm{Ca (s)} $$ The standard reduction potential for this half-reaction, \(E^{\circ}\), is \(-2.87~V\). Since voltage is an intensive property, it does not depend on efficiency. Therefore, the minimum voltage needed to cause electrolysis is equal to the standard reduction potential \(E^{\circ}\), which is \(-2.87~V\).

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

A voltaic cell utilizes the following reaction and operates at 298 K: $$ 3 \mathrm{Ce}^{4+}(a q)+\mathrm{Cr}(s) \longrightarrow 3 \mathrm{Ce}^{3+}(a q)+\mathrm{Cr}^{3+}(a q) $$ (a) What is the emf of this cell under standard conditions? (b) What is the emf of this cell when \(\left[\mathrm{Ce}^{4+}\right]=3.0 \mathrm{M},\) \(\left[\mathrm{Ce}^{3+}\right]=0.10 \mathrm{M},\) and \(\left[\mathrm{Cr}^{3+}\right]=0.010 \mathrm{M} ?(\mathbf{c})\) What is the emf of the cell when $\left[\mathrm{Ce}^{4^{+}}\right]=0.010 \mathrm{M},\left[\mathrm{Ce}^{3+}\right]=2.0 \mathrm{M}$ and \(\left[\mathrm{Cr}^{3+}\right]=1.5 \mathrm{M} ?\)

(a) What is electrolysis? (b) Are electrolysis reactions thermodynamically spontaneous? (c) What process occurs at the anode in the electrolysis of molten \(\mathrm{NaCl}\) ? (d) Why is sodium metal not obtained when an aqueous solution of \(\mathrm{NaCl}\) undergoes electrolysis?

Complete and balance the following equations, and identify the oxidizing and reducing agents. (Recall that the \(\mathrm{O}\) atoms in hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\), have an atypical oxidation state.) (a) $\mathrm{NO}_{2}^{-}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{NO}_{3}^{-}(a q)$ (acidic solution) (b) $\mathrm{S}(s)+\mathrm{HNO}_{3}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{3}(a q)+\mathrm{N}_{2} \mathrm{O}(g)$ (acidic solution) (c) $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{CH}_{3} \mathrm{OH}(a q) \longrightarrow \mathrm{HCOOH}(a q)+ \mathrm{Cr}^{3+}(a q)$ (acidic solution) (d) $\mathrm{BrO}_{3}^{-}(a q)+\mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{Br}^{-}(a q)+\mathrm{N}_{2}(g)$ (acidic solution) (e) $\mathrm{NO}_{2}^{-}(a q)+\mathrm{Al}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{AlO}_{2}^{-}(a q)$ (basic solution) (f) $\mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{ClO}_{2}(a q) \longrightarrow \mathrm{ClO}_{2}^{-}(a q)+\mathrm{O}_{2}(g)$ (basic solution)

A common shorthand way to represent a voltaic cell is anode \(\mid\) anode solution || cathode solution \(\mid\) cathode A double vertical line represents a salt bridge or a porous barrier. A single vertical line represents a change in phase, such as from solid to solution. (a) Write the half-reactions and overall cell reaction represented by $\mathrm{Fe}\left|\mathrm{Fe}^{2+}\right|\left|\mathrm{Ag}^{+}\right| \mathrm{Ag} ;$ calculate the standard cell emf using data in Appendix E. (b) Write the half-reactions and overall cell reaction represented by $\mathrm{Zn}\left|\mathrm{Zn}^{2+}\right|\left|\mathrm{H}^{+}\right| \mathrm{H}_{2} ;$ calculate the standard cell emf using data in Appendix E and use Pt for the hydrogen electrode. (c) Using the notation just described, represent a cell based on the following reaction: $$ \begin{aligned} \mathrm{ClO}_{3}^{-}(a q)+3 \mathrm{Cu}(s) &+6 \mathrm{H}^{+}(a q) \\ & \longrightarrow \mathrm{Cl}^{-}(a q)+3 \mathrm{Cu}^{2+}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ \(\mathrm{Pt}\) is used as an inert electrode in contact with the \(\mathrm{ClO}_{3}^{-}\) and \(\mathrm{Cl}^{-}\). Calculate the standard cell emf given: \(\mathrm{ClO}_{3}^{-}(a q)+\) $6 \mathrm{H}^{+}(a q)+6 \mathrm{e}^{-} \longrightarrow \mathrm{Cl}^{-}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) ; E^{\circ}=1.45 \mathrm{~V}$

A student designs an ammeter (device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the device for 90 min, \(32.5 \mathrm{~mL}\) of water-saturated \(\mathrm{H}_{2}(g)\) is collected. The temperature of the system is \(20^{\circ} \mathrm{C},\) and the atmospheric pressure is \(101.3 \mathrm{kPa}\). What is the magnitude of the average current in amperes?
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

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