Extra Credit 49

17.7.3

How long would it take to reduce 1 mole of each of the following ions using the current indicated? Assume the voltage is sufficient to perform the reduction.

1. Al³⁺, 1.234 A
2. Ca²⁺, 22.2 A
3. Cr⁵⁺, 37.45 A
4. Au³⁺, 3.57 A

Solution:

In this problem a external voltage is applied to a non-spontaneous reaction in order to drive the reaction. The relationship between current, charge, and time is C=At

C is the charge of the reaction in Coulombs, A is current in amps, and t is time in seconds.

A) To find the time of the reduction rearrange the equation to t= C/A

C= (3 mol e^-)(96485sA/mol e^-), This is found by balancing the reduction equation to find the electrons transferred in Al³⁺ is Al³⁺+3e^-⇒ Al , the moles of electrons is then multiplied by Faraday's constant to convert it in to Coulombs

A= 1.23A

t= unknown

t= (3mol e^-)(96485As/mol e^-)/1.23A

t= 2.346E⁵ seconds

B) Ca²⁺+2e^-⇒Ca balanced reduction formula

C= (2mol e^-)(96485As/mol e^-)

A= 22.2A

t=(2mol e^-)(96485As/mol e^-)/22.2A

t=8692.3 seconds

C) Cr⁵⁺+5e^-⇒Cr balanced reduction formula

C= (5mol e^-)(96485 As/mol e^-)

A=37.45

t= (5mol e^-)(96485 As/mol e^-)/37.45 A

t= 1.288E⁴ seconds

D) Au³⁺+3e^-⇒Au balanced reduction formula

C= (3mol e^-)(96485 As/mol e^-)

A= 3.57 A

t= (3mol e^-)(96485 As/mol e^-)/3.57 A

t= 8.11E⁴ seconds

12.3.12

Under certain conditions the decomposition of ammonia on a metal surface gives the following data:

Determine the rate equation, the rate constant, and the overall order for this reaction.

Solution:

The decomposition of ammonia on a metal surface is 2NH₃⇒N₂+3H₂

From the table above it you can tell that this reaction is a zero order reaction because the change in concentration of ammonia does not effect the reaction rate of the decomposition. If the reaction rate did change then you would find the overall order of the reaction by setting the rate constant formulas of two equation equal to each other to find what power the ratio of the concentrations is raised to and that is the overall order of the reaction.

The rate equation for this decomposition is Rate =K[NH₃]⁰

The Rate Constant is 1.5E^-6=K[1E^-3]⁰

K=1.6E^-6 (mol/L/h)

12.6.4

Define these terms:

1. unimolecular reaction
2. bimolecular reaction
3. elementary reaction
4. overall reaction

Solution

1) A unimolecular reaction is a first order reaction in which one molecule rearranges its self to produce one or more products. It is an elementary reaction that has no intermediates and only has one transition state. An example of a unimolecular reaction is radioactive decay.

A→products

Rate=K[A]

2) A bimolecular reaction is the collision of two particles that exchange energy, atoms, or groups of atoms. It is one of the most common reactions for organic reactions. This reaction is a second order reaction

2B→ products Rate =K[B]²

A+B→ products Rate= K[A][B]

3) An elementary reaction is a single step reaction that has a single transition state without any intermediates. A complex reaction is the collection of multiple elementary reactions. They cannot be broken down into simpler reactions.

4) Overall reaction is the combination of multiple elementary reactions to create a complex reaction. The elementary reactions add up to give an overall balanced equation for the reaction. The reaction rate for this overall reaction is determined by the rate of the slowest elementary reaction.

21.4.16

The isotope ²⁰⁸Tl undergoes β decay with a half-life of 3.1 min.

1. What isotope is produced by the decay?
2. How long will it take for 99.0% of a sample of pure ²⁰⁸Tl to decay?
3. What percentage of a sample of pure ²⁰⁸Tl remains un-decayed after 1.0 h?

Solution:

1) β decay is a type of radioactive decay in which a atom emits a electron or a positron and a neutrino. The balanced equation for this decay is

²⁰⁸Tl→ ²⁰⁸Pb+_-1⁰e The isotope produced is ²⁰⁸Pb

2) To find the half life rate use the equation y=Pe^rt (y= the amount of sample un-decayed, P= the original amount of sample, r= rate, t= time)

50=100e^r(3.1)

r= ln(.5)/3.1 = -.22359

Now use the rate to find how long it will take for 99% of the sample to decay (which means only 1% of the sample remains)

1=100e^-.22359t

t= ln(1/100)/-.22359 = 20.60 minutes for 99% of the sample to decay

3) To find the unknown percentage of sample remaining use the same equation as above with the same rate of decay

y=100e^{(-.22359)(60min)}

y= 1.49E^-4 % remains un-decayed after one hour

20.3.4

What is the purpose of a salt bridge in a galvanic cell? Is it always necessary to use a salt bridge in a galvanic cell?

Solution:

A salt bridge is a U-shaped tube or string that is inserted into both solutions of a galvanic cell and contains a concentrated liquid or gelled electrolyte (Na⁺,K⁺, NO₃^-, SO₄^-2). The purpose of a salt bridge in a galvanic cell is to complete the electrical circuit by carrying the electrical charge between the two cells. It also maintains the electrical neutrality in both compounds by allowing ions to migrate between them. Without a salt bridge, the reaction would rapidly cease because electrical neutrality could not be maintained.

20.5.15

Based on Table 19.2 and Chapter 29 "Appendix E: Standard Reduction Potentials at 25°C", do you agree with the proposed potentials for the following half-reactions? Why or why not?

1. Cu²⁺(aq) + 2e⁻ → Cu(s), E° = 0.68 V
2. Ce⁴⁺(aq) + 4e⁻ → Ce(s), E° = −0.62 V

Solution:

1) Based on the two tables listed above I do not agree with the proposed potentials because in both tables E^°= .3419 V and the E°_cell for reduction potentials do not change because it is the potential of a cell measured under standard conditions, standard states, and at a fixed temperature. Only the E_cell values change.

2) Based on the two tables listed above I do not agree with the proposed potentials because in both tables the E^°_cell= 1.72 V for Ce⁴⁺+4e^-→Ce

14.1.1

What information can you obtain by studying the chemical kinetics of a reaction? Does a balanced chemical equation provide the same information? Why or why not?

Solution:

From studying the chemical kinetics of a reaction you can determine the reaction rate of the reaction and the speed of the reaction. From the chemical kinetics of a reaction you can also learn about the mechanisms of the reaction and which elementary reaction determines the overall reaction rate of the complex reaction. A balanced chemical equation does not provide the same information because the equation can only tell you if the reaction is possible, spontaneous or non-spontaneous, and the stoichiometry of the reaction but not when the reaction will react or the speed of the reaction.

14.4.8

1-Bromopropane is a colorless liquid that reacts with S₂O₃²⁻ according to the following reaction:

C₃H₇Br + S₂O₃²⁻ → C₃H₇S₂O₃⁻ + Br⁻

The reaction is first order in 1-bromopropane and first order in S₂O₃²⁻, with a rate constant of 8.05 × 10⁻⁴ M⁻¹·s⁻¹. If you began a reaction with 40 mmol/100 mL of C₃H₇Br and an equivalent concentration of S₂O₃²⁻, what would the initial reaction rate be? If you were to decrease the concentration of each reactant to 20 mmol/100 mL, what would the initial reaction rate be?

Solution:

The initial reaction rate is

Rate= K[C₃H₇Br]¹[S₂O₃^2-]¹

Rate= (8.05E^-4 M^-1s^-1)[.4M][.4M]

Rate= 1.29E^-4 Ms^-1

Decreased concentration reaction rate

Rate =K[C₃H₇Br]¹[S₂O₃^2-]¹

Rate=(8.05E^-4 M^-1s^-1)[.2M][.2M]

Rate= 3.22E^-5Ms^-1