Animated Solution for Chemistry - Metallurgy: The correct statement regarding the given Ellingham diagram is

Imagine you are an ancient metallurgist trying to extract pure metal from a stubborn rock. You throw it in a fire, add some charcoal, and hope for the best. Sometimes it works, sometimes it doesn't. Fast forward to the 20th century, and physical chemist Harold Ellingham gave us a master key to unlock these metallurgical mysteries: The Ellingham Diagram.

This diagram is essentially a map of thermodynamic stability. It plots the standard Gibbs free energy of formation ($\Delta G^{\circ }$) of various metal oxides against temperature ($T$). The core equation governing this is the famous thermodynamic relation:

When a metal oxidizes, it typically consumes oxygen gas to form a solid oxide. Because a gas is being converted into a solid, the randomness or entropy of the system decreases ($\Delta S^{\circ }<0$). Since the $-T\Delta S^{\circ }$ term becomes positive as temperature increases, the overall $\Delta G^{\circ }$ becomes less negative. This is why almost all metal oxidation curves slope upwards!

The most crucial takeaway from the Ellingham diagram is a simple visual rule: The Lower Curve Reduces the Upper Curve.

Why? Because a lower position on the y-axis means a more negative $\Delta G^{\circ }$. A more negative $\Delta G^{\circ }$ implies that the oxide is thermodynamically more stable. Therefore, a metal whose curve is lower has a stronger affinity for oxygen than a metal whose curve is higher. If you mix the lower metal with the upper metal's oxide, the lower metal will aggressively steal the oxygen, leaving the upper metal in its pure, reduced state.

Let's apply our golden rule to the options provided in the question.

Option (a): At $800^{\circ }\text{C}$, Cu can be used for the extraction of Zn from ZnO. If we look at the vertical line corresponding to $800^{\circ }\text{C}$, we see that the curve for Copper ($\text{Cu}$) is situated significantly higher than the curve for Zinc ($\text{Zn}$). Because Copper's curve is above Zinc's, Copper has a weaker affinity for oxygen. It cannot steal oxygen from Zinc. Thus, this statement is incorrect.

Option (c): At $500^{\circ }\text{C}$, coke can be used for the extraction of Zn from ZnO. Coke is essentially Carbon ($\text{C}$). At $500^{\circ }\text{C}$, the curve for the oxidation of Carbon to Carbon Monoxide ($2\text{C}+{\text{O}}_2\to 2\text{CO}$) is still above the Zinc curve. Therefore, at this relatively low temperature, Carbon is not a strong enough reducing agent to extract Zinc. This statement is incorrect.

Option (d): Coke cannot be used for the extraction of Cu from ${\text{Cu}}_2\text{O}$. If we observe the Carbon curve and the Copper curve, we notice that the Carbon curve is below the Copper curve across the entire temperature range shown (from $500^{\circ }\text{C}$ onwards). Because Carbon is lower, it can easily reduce Copper oxide. The statement claims it cannot, making the statement itself incorrect.

Option (b): At $1400^{\circ }\text{C}$, Al can be used for the extraction of Zn from ZnO. Finally, let's look at Aluminum ($\text{Al}$). The Aluminum curve is positioned at the very bottom of the provided diagram. It is below the Zinc curve at all temperatures, including $1400^{\circ }\text{C}$. Because Aluminum's oxide is vastly more stable than Zinc's oxide, Aluminum will readily reduce $\text{ZnO}$ to pure Zinc. This statement is absolutely correct!

As a side note, did you notice that the Carbon curve is the only one sloping downwards? When solid carbon reacts with oxygen gas to form carbon monoxide gas, the number of moles of gas increases. This means entropy increases ($\Delta S^{\circ }>0$). Consequently, the $-T\Delta S^{\circ }$ term becomes increasingly negative as temperature rises, causing the curve to plunge downwards. This unique property is why Carbon (coke) becomes a universal reducing agent at high temperatures—eventually, its curve will cross below almost every metal oxide curve!