Zirconium is one of the few metals that retains its...

Zirconium is one of the few metals that retains its structural integrity upon exposure to radiation. For this reason, the fuel rods in most nuclear reactors are made of zirconium. Answer the following questions about the redox properties of zirconium based on the half-reaction $\mathrm{ZrO}_{2} \cdot \mathrm{H}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}+4 \mathrm{e}^{-} \longrightarrow \mathrm{Zr}+4 \mathrm{OH}^{-} \quad \mathscr{E}^{\circ}=-2.36 \mathrm{~V}$ a. Is zirconium metal capable of reducing water to form hydrogen gas at standard conditions? b. Write a balanced equation for the reduction of water by zirconium metal. c. Calculate $\mathscr{8}^{\circ}, \Delta G^{\circ}$, and $K$ for the reduction of water by zirconium metal. d. The reduction of water by zirconium occurred during the accident at Three Mile Island, Pennsylvania, in $1979 .$ The hydrogen produced was successfully vented and no chemical explosion occurred. If $1.00 \times 10^{3} \mathrm{~kg} \mathrm{Zr}$ reacts, what mass of $\mathrm{H}_{2}$ is produced? What volume of $\mathrm{H}_{2}$ at $1.0 \mathrm{~atm}$ and $1000 .{ }^{\circ} \mathrm{C}$ is produced? e. At Chernobyl, USSR, in 1986 , hydrogen was produced by the reaction of superheated steam with the graphite reactor core: $$\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$$ A chemical explosion involving the hydrogen gas did occur at Chernobyl. In light of this fact, do you think it was a correct decision to vent the hydrogen and other radioactive gases into the atmosphere at Three Mile Island? Explain.

Zirconium is one of the few metals that retains its structural integrity upon exposure to radiation. For this reason, the fuel rods in most nuclear reactors are made of zirconium. Answer the following questions about the redox properties of zirconium based on the half-reaction
$\mathrm{ZrO}_{2} \cdot \mathrm{H}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}+4 \mathrm{e}^{-} \longrightarrow \mathrm{Zr}+4 \mathrm{OH}^{-} \quad \mathscr{E}^{\circ}=-2.36 \mathrm{~V}$
a. Is zirconium metal capable of reducing water to form hydrogen gas at standard conditions?
b. Write a balanced equation for the reduction of water by zirconium metal.
c. Calculate $\mathscr{8}^{\circ}, \Delta G^{\circ}$, and $K$ for the reduction of water by zirconium metal.
d. The reduction of water by zirconium occurred during the accident at Three Mile Island, Pennsylvania, in $1979 .$ The hydrogen produced was successfully vented and no chemical explosion occurred. If $1.00 \times 10^{3} \mathrm{~kg} \mathrm{Zr}$ reacts, what mass of $\mathrm{H}_{2}$ is produced? What volume of $\mathrm{H}_{2}$ at $1.0 \mathrm{~atm}$ and $1000 .{ }^{\circ} \mathrm{C}$ is produced?
e. At Chernobyl, USSR, in 1986 , hydrogen was produced by the reaction of superheated steam with the graphite reactor core:
$$\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$$
A chemical explosion involving the hydrogen gas did occur at Chernobyl. In light of this fact, do you think it was a correct decision to vent the hydrogen and other radioactive gases into the atmosphere at Three Mile Island? Explain.

Key Concepts

Redox Reactions

Redox reactions involve the transfer of electrons between species, with one substance being oxidized (losing electrons) and the other being reduced (gaining electrons). Understanding half-reactions and the overall balancing of electron transfer is central to predicting reaction feasibility and products.

Thermodynamics in Electrochemistry

The relationship between the cell potential, Gibbs free energy change (?G), and the number of electrons transferred is critical in electrochemistry. The equation ?G = -nFE links the electrochemical potential (E) with the thermodynamic feasibility of a reaction, indicating whether a reaction is spontaneous.

Equilibrium Constant and the Nernst Equation

The equilibrium constant (K) of an electrochemical reaction can be derived from the Gibbs free energy change and the standard cell potential. The Nernst equation further allows for the calculation of cell potential under non-standard conditions, bridging thermodynamics with kinetics and equilibrium in redox systems.

Stoichiometry and Gas Laws in Redox Processes

Applying stoichiometry to redox reactions, including the conversion of moles to mass and volume (especially when gases are involved), is essential. The ideal gas law connects the amount (in moles) and conditions of temperature and pressure to the volume of gases produced in a reaction.

Standard Reduction Potentials

Standard reduction potentials provide a measure of the tendency of a chemical species to acquire electrons and be reduced under standard conditions. They are important for determining whether a given redox reaction will be spontaneous, as a higher (or less negative) reduction potential indicates a greater driving force for reduction.

Transcript

00:01 Let's see if we can answer this rather giant question.

00:03 We are asked to consider zirconium and we're asked for our first question, a.

00:10 Is zirconium metal capable of reducing water to form hydrogen gas at standard conditions? and i'm going to think that this is probably going to be a yes.

00:53 So is it capable of reducing this? i'm going to call this reaction one.

01:01 Reaction one, we would have to reverse.

01:06 So it would be e would equal plus 2 .36 volts.

01:12 And my second reaction would have to be reducing water.

01:28 That would be h2 plus 2oh minus and this is negative, e for this cell is negative 0 .83.

01:53 So my e for my cell will be equal to negative 0 .83 plus 2 .36, and that will be 1 .53.

02:36 So this means that zirconium is capable of acting to reduce water.

03:05 Okay, there's my first question.

03:13 Let's go to my second question.

03:21 B.

03:24 Write the balanced equation for reduction of water.

03:28 Hmm.

03:30 Balanced equation for the reduction of water.

03:42 I.

03:43 Zirconium.

03:45 Ok.

03:49 And let's get right here.

03:51 So i will have h2o and i will have let's get over here back to my equation so i can see it.

04:16 I'll have zirconium plus 4 oh, and this will be zro2, 4 e minus.

04:43 Then i'm going to take this equation times 2 to get 4, 4, 2, and 4.

04:57 So my ohs will cross out, and i will end up with 1 zirconium plus one two three four three h2o and i get a zr o2 dot h2o plus two h2 i think this was an s this is an l okay that one wasn't so hard c back to c find e cell didn't i already do this delta g and k.

06:10 My e cell, i already did one problem, it was positive 1 .53 volts.

06:17 We did that in part a.

06:21 And then our delta g will be equal to negative nfe minus.

06:29 So my delta g will be equal to, remember from up here we had four moles of electrons times faraday's which is 96485 c over moles of electrons times 1 .53.

06:54 4 times 96485 times 1 .353.

07:01 And then i like to multiply this by 1000 joules per kilojoule.

07:13 And for my volts, i'm going to put my 1 .53 j over c there.

07:23 So my delta g would be equal to negative 590 .5 kilojoules.

07:34 And now my k is equal to the antilog of my, let me see here, my k is equal to my antilog of 4 times 1 .53 divided by 0 .0592.

08:23 Let me try this.

08:27 Second e.

08:28 4, this should be minus, times 1 .53 divided by 0 .0592.

08:37 4 times 1 .53 divided by 0 .0592 is 103 .4.

08:59 Let's try the anti -log of the second answer...