Question

Zirconium is one of the few metals that retains its structural integrity upon exposure to radiation. The fuel rods in most nuclear reactors therefore are often 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. c. Calculate \(\mathscr{E}^{\circ}, \Delta G^{\circ}\), and \(K\) for the reduction of water by zirconium metal. d. The reduction of water by zirconium occurred during the accidents at Three Mile Island in \(1979 .\) The hydrogen produced was successfully vented and no chemical explosion occurred. If \(1.00 \times 10^{3} \mathrm{~kg}\) 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 in 1986, hydrogen was produced by the reaction of superheated steam with the graphite reactor core: $$ \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g) $$

Short answer

In summary, Zirconium is capable of reducing water to hydrogen gas under standard conditions with a standard potential of -2.36V. The balanced equation for the reduction of water by Zirconium is \(2ZrO_2 \cdot H_2O + 2H_2O \longrightarrow 2Zr + 2H_2 + 4OH^-\). The calculated values for the reaction are \(\mathscr{E}^{\circ} = -2.36 V\), \(\Delta G^{\circ} = 909,717 J/mol\), and \(K = 3.53 × 10^{50}\). In the specific scenario provided, the produced hydrogen has a mass of 22g and a volume of 920L. At the Chernobyl incident, hydrogen was produced by the reaction between superheated steam and the graphite reactor core.

Step-by-step solution

Compare standard reduction potentials

To determine if Zirconium can reduce water to hydrogen gas, we must compare the standard reduction potential of Zirconium to the standard reduction potential of water. For water, the standard reduction potential is \(E^{\circ}_{H_2O} = 0V\). Since the given standard potential of Zirconium is \(E^{\circ}_{Zr} = -2.36V\), it is less than that of water. Therefore, Zirconium can reduce water to hydrogen gas under standard conditions, since a negative reduction potential implies that the reaction is spontaneous and feasible. #b. Balanced equation for reduction of water#

Write balanced equation

To write the balanced equation for the reduction of water by Zirconium, we first express the half-reactions for Zirconium and water: Zirconium: \[ZrO_2 \cdot H_2O + H_2O + 4e^- \to Zr + 4OH^-\] Water: \[2H_2O + 2e- \to H_2 + 2OH^-\] Now we must balance the half-reactions by equating the number of electrons in each: Zirconium: \(4e^-\) Water: \(2 \times 2e^-=4e^-\) Finally, we add the balanced half-reactions: \[2(ZrO_2 \cdot H_2O + H_2O) \to 2Zr + 8OH^-\] \[4H_2O + 4e^- \to 2H_2 + 4OH^-\] \square \[\boxed{2ZrO_2 \cdot H_2O + 2H_2O \longrightarrow 2Zr + 2H_2 + 4OH^- }\] #c. Calculation of E, ΔG, and K for reduction of water by Zirconium#

Nernst equation and standard equation

To calculate these values, we utilize the Nernst equation for E: \[E = E^{\circ} - \frac{RT}{nF} \ln{Q}\] For the standard potential, since the only electron transfer involved is of Zirconium reducing water which has \(E^{\circ}_{Zr} = -2.36V\), we have \(E^{\circ} = -2.36V\). For the Gibbs free energy, we use the relation: \[\Delta G^{\circ} = -nFE^{\circ}\] Where: n = 4 moles of electrons F = 96485 C/mol (Faraday's constant) Plugging the values, we get: \[\Delta G^{\circ} = -4(96485)(-2.36) J/mol = 909,717 J/mol\] For the equilibrium constant K, we use the relationship: \[K = e^{-\Delta G^{\circ}/(RT)}\] Where: R = 8.314 J/mol ⋅ K (gas constant) T = 298 K (standard conditions) \[K = e^{-909717/(8.314 × 298)} = 3.53 × 10^{50}\] Hence, for the reduction of water by Zirconium, we have: \(\mathscr{E}^{\circ} = -2.36 V\) \(\Delta G^{\circ} = 909,717 J/mol\) \(K = 3.53 × 10^{50}\) #d. Calculation of mass and volume of hydrogen produced#

Moles and volume of hydrogen

Given the reaction involves \(1.00 \times 10^3 kg\) of Zirconium, we can determine the amount of hydrogen produced using stoichiometry: Molecular weight of Zr: \[91g/mol\] Moles of Zirconium: \[\frac{1.00 \times 10^3 kg}{91g} \times \frac{1mol}{1000g} = 11mol\] Since the balanced equation is \(2ZrO_2 \cdot H_2O + 2H_2O \longrightarrow 2Zr + 2H_2 + 4OH^-\), every 2 moles of Zirconium will produce 2 moles of hydrogen gas Moles of hydrogen produced: \[\frac{11mol}{2} \times 2 = 11mol\] Mass of hydrogen produced: \[11mol \times \frac{2g}{1mol} = 22g\] To find the volume of hydrogen, we use the ideal gas law equation \(PV=nRT\): Volume of hydrogen produced: \[V=\frac{nRT}{P}\] Where P = 1 atm R = 0.0821 L ⋅ atm/mol ⋅ K T = 1273 K (given as 1000°C, but we must convert to Kelvin) \[V = \frac{11(0.0821)(1273)}{1} L = 920 L\] Hence, the produced hydrogen has: Mass \(= 22g\) Volume \(= 920 L\) #e. Hydrogen production at Chernobyl#

Mention reaction at Chernobyl

The hydrogen production at Chernobyl occurred due to the following reaction: \[C(s) + H_2O(g) \longrightarrow CO(g) + H_2(g)\] At Chernobyl, the reaction occurred between superheated steam and the graphite reactor core, producing hydrogen gas.

Key concepts

Zirconium

Zirconium is known for its resistance to heat and corrosion, making it ideal for use in nuclear reactors where it often serves as the material for fuel rods. This metal maintains its structural integrity even when exposed to neutron radiation. This unique property of zirconium plays a pivotal role in its application within the nuclear industry. Moreover, zirconium reacts with water in redox processes to reduce it forming hydrogen gas. These reactions are important to understand as they relate to safety considerations in nuclear power plants. Recognizing zirconium's redox reactions helps in assessing the risks and mechanisms involved in hydrogen production, especially during nuclear accidents.

Nuclear Chemistry

Nuclear chemistry focuses on the chemical processes that occur in nuclear reactors. Key processes involve the use of elements like zirconium, which as previously mentioned, can support high radiation conditions. In the context of nuclear accidents, like those at Three Mile Island and Chernobyl, understanding redox reactions involving zirconium and the production of hydrogen gas is crucial.
These accidents highlight the importance of knowing how materials behave under extreme conditions. For instance, at Three Mile Island, zirconium reacted to form hydrogen, which, if not properly vented, could pose an explosive hazard. At Chernobyl, the interaction between steam and graphite produced hydrogen through a different reaction, exacerbating the reactor meltdown.
Thus, nuclear chemistry does not only involve reactions for energy production but also necessitates foresight in managing by-products like hydrogen for nuclear safety.

Electrochemistry

Electrochemistry studies the relationship between electrical energy and chemical change. In the case of zirconium reactions, redox potentials play a critical role. The standard reduction potential ( E^{ extdegree} ) of a substance indicates its ability to gain electrons.
For zirconium, a negative E^{ extdegree} value (-2.36V) indicates that it can donate electrons, reducing water to hydrogen gas under specific conditions. This interdependence of electrical and chemical properties helps predict and control reactions in electrochemical cells, which is not only vital in electronic devices but in managing reactions in nuclear reactors as well.

• A negative standard potential suggests a more spontaneous redox reaction under standard conditions.
• Understanding zirconium’s electrochemical properties ensures better predictions and precautions in real-world applications, like nuclear reactors.

Gibb's Free Energy

Gibb's Free Energy ( ΔG^{ extdegree} ) is a concept in thermodynamics that signifies a system's potential to perform work, particularly chemical work during reactions. It links directly to the spontaneity of redox reactions involving zirconium.
For zirconium's reaction with water, the calculated ΔG^{ extdegree} was positive, which signifies a non-spontaneous process under standard conditions. However, the high stored energy in these systems at elevated temperatures could make certain reactions feasible. ΔG^{ extdegree} also helps estimate the equilibrium constant ( K ) of the reaction, which gives insights into the extent of a reaction occurring.

• A positive ΔG^{ extdegree} value typically implies that energy must be added for the reaction to proceed.
• High temperatures and pressures in nuclear reactors can affect ΔG^{ extdegree} , making certain reactions possible that otherwise wouldn't occur at standard conditions.

Understanding ΔG^{ extdegree} allows engineers to evaluate and control the chemical reactions in nuclear reactor systems for efficient and safe operations.