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 $$ \mathrm{ZrO}_{2} \cdot \mathrm{H}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}+4 \mathrm{e}^{-} \longrightarrow \mathrm{Zr}+4 \mathrm{OH}^{-} \quad 8^{\circ}=-2.36 \mathrm{V} $$ 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 \(\mathscr{G} \circ, \Delta G^{\circ},\) 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 \(1.00 \times 10^{3} \mathrm{kg}\) Zreacts, 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: $$ \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g) $$ It was not possible to prevent a chemical explosion at Chernobyl. In light of this, do you think it was a correct decision to vent the hydrogen and other radioactive gases into the atmosphere at Three Mile Island? Explain.

Short answer

Zirconium can reduce water to form hydrogen gas at standard conditions, and the balanced equation for this reaction is: $$ \mathrm{ZrO_2 \cdot H_2O + Zr + 2H_2O} \longrightarrow 2\mathrm{Zr} + 4 \mathrm{OH^{-}} + \mathrm{H}_{2}(g)$$ The standard Gibbs free energy change is 295,261 J/mol, the reaction Gibbs free energy change is the same, the equilibrium constant is \(1.5 \times 10^{-25}\). When 1.00 x 10^3 kg of zirconium reacts, 1.11 x 10^4 g of hydrogen gas and 5.78 x 10^5 L of hydrogen gas at 1.0 atm and 1000 °C is produced. Venting hydrogen and other radioactive gases at Three Mile Island was a correct decision to prevent an explosion similar to what happened at Chernobyl and reduce further damage and potential loss of life.

Step-by-step solution

c. Calculating standard Gibbs free energy change, reaction Gibbs free energy change, and the equilibrium constant

From the given standard reduction potentials, we can calculate the standard electromotive force (EMF) of the reaction: $$ E^{\circ} = -2.36\,V - (-0.83\,V) = -1.53\,V $$ To obtain the standard Gibbs free energy change, we use the equation: $$ \Delta G^{\circ} = -nFE^{\circ} $$ Where n = 2 mol of electrons transferred, F is Faraday's constant (96,485 C/mol), and E^{\circ} = -1.53 V $$ \Delta G^{\circ} = -(2)(96,485\,\frac{\mathrm{C}}{\mathrm{mol}})(-1.53\,\mathrm{V}) = 295,261 \,\frac{\mathrm{J}}{\mathrm{mol}} $$ Now to calculate the equilibrium constant (K) we can use: $$ K = \mathrm{e}^{-\frac{\Delta G^{\circ}}{RT}} $$ Where R is the ideal gas constant (8.314 J/(mol K)) and T is the temperature (298 K) $$ K = \mathrm{e}^{-\frac{295,261\,\frac{\mathrm{J}}{\mathrm{mol}}}{(8.314\,\frac{\mathrm{J}}{\mathrm{mol\,K}})(298\,\mathrm{K})}} = 1.5 \times 10^{-25} $$

d. Mass and volume of hydrogen gas produced

To find the mass of hydrogen gas produced from the reaction of 1.00 x 10^3 kg of zirconium, we start by calculating the moles of zirconium: $$ \mathrm{moles\,of\,Zr} = \frac{1.00 \times 10^3 \,\mathrm{kg}}{91.22\,\frac{\mathrm{g}}{\mathrm{mol}}} = 1.10 \times 10^4 \,\mathrm{mol} $$ From the balanced equation, we know that 1 mole of zirconium produces 0.5 moles of hydrogen gas. So we find the moles of hydrogen gas produced: $$ \mathrm{moles\,of\,H_{2}} = (0.5)(1.10 \times 10^4 \,\mathrm{mol}) = 5.50 \times 10^3 \mathrm{mol} $$ Now we can find the mass of hydrogen gas produced: $$ \mathrm{mass\,of\,H_{2}} = (5.50 \times 10^3 \,\mathrm{mol})(2.02\,\frac{\mathrm{g}}{\mathrm{mol}}) = 1.11 \times 10^4\,\mathrm{g} $$ To find the volume of hydrogen gas produced at 1.0 atm and 1000 °C, we can use the ideal gas law: $$ PV = nRT $$ Where P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature. $$ (1.0\,\mathrm{atm})V = (5.50 \times 10^3\,\mathrm{mol})(0.0821\,\mathrm{L\,atm/mol\,K})(1273\,\mathrm{K}) $$ $$ V = 5.78 \times 10^5\,\mathrm{L} $$

e. Venting decision at Three Mile Island

At Three Mile Island, although venting the hydrogen and other radioactive gases into the atmosphere would have environmental risks, it prevented a chemical explosion similar to what happened at Chernobyl. In Chernobyl, hydrogen was produced by the reaction of superheated steam with the graphite reactor core, which resulted in a chemical explosion. Venting the hydrogen gas produced at Three Mile Island ensured that a chemical explosion did not occur. Considering the alternatives, it was a correct decision to vent the hydrogen and other radioactive gases into the atmosphere at Three Mile Island to prevent further damage and potential loss of life.

Key concepts

Zirconium

Zirconium is a unique metal that has excellent properties, making it ideal for use in nuclear reactors. Due to its ability to withstand radiation without losing structural integrity, zirconium is often used to create fuel rods.
These rods play a vital role in containing nuclear materials safely, ensuring that the reactor operates efficiently and without leakage of hazardous materials.

When considering zirconium's redox properties, it's crucial to understand how it interacts with other substances, such as water. A redox reaction involves the transfer of electrons, with zirconium potentially acting as a reducing agent.
This means zirconium can give electrons to other elements or compounds, leading to a change in their oxidation state.

In the context of nuclear chemistry, such properties are beneficial because they allow zirconium to participate in various reactions without deteriorating quickly. Its stable properties under high radiation and temperature make it an essential component in the safe operation of nuclear power plants.

Gibbs Free Energy

Gibbs Free Energy is a scientific concept that helps us understand the feasibility of a reaction. It indicates whether a reaction can occur spontaneously under constant temperature and pressure conditions.
In a redox reaction like the one involving zirconium, Gibbs Free Energy (\( \Delta G^{\circ}\)), derived from the reaction's electromotive force (EMF), tells us about the energy changes that occur.

The equation \( \Delta G^{\circ} = -nFE^{\circ}\) allows us to calculate the standard Gibbs free energy change, where \(n\) is the number of moles of electrons transferred in the reaction, \(F\) is the Faraday constant, and \(E^{\circ}\) is the standard EMF.
If the value of \(\Delta G^{\circ}\) is negative, the reaction can proceed without external energy input, signaling its spontaneity.

In nuclear chemistry, understanding Gibbs Free Energy is crucial in predicting and controlling reactions within the reactor. It ensures that the reactions involved in energy production are both manageable and efficient, reducing the risk of unexpected chain reactions, which could be dangerous.

Nuclear Chemistry

Nuclear chemistry involves the study of chemical processes that do not simply change chemical characteristics but involve alterations at the atomic nucleus level. This field has significant applications in energy production through nuclear reactors.
In these reactors, materials like zirconium are used because they can withstand the intense radiation and heat produced during fission reactions.

One of the key components in nuclear reactors is redox reactions, which can affect both the fuel material and surrounding components like zirconium fuel rods.
Understanding these reactions helps in ensuring the reactor's safety and efficiency.

Significant nuclear events such as those at Three Mile Island and Chernobyl highlight the importance of managing the chemical and nuclear reactions carefully. For example, at Three Mile Island, preventing a chemical explosion involved understanding the redox reactions and strategically venting gases.
This decision demonstrates the delicate balance necessary in nuclear chemistry, ensuring that power generation remains safe for both the environment and human health.