Problem 26 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Impure nickel metal is purified using the Mond process where it is first reacted at \(80^{\circ} \mathrm{C}\) with carbon monoxide to form \(\mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g})\) $$\mathrm{Ni}(\mathrm{s})+4 \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g})$$ followed by heating to \(200^{\circ} \mathrm{C}\) when the reverse reaction occurs. Use the following thermodynamic data to show that this approach is thermodynamically feasible. $$\begin{array}{llll} & \mathrm{Ni}(\mathrm{s}) & \mathrm{Ni}(\mathrm{CO})_{4}(\mathrm{g}) & \mathrm{CO}(\mathrm{g}) \\\\\Delta_{1} \mathrm{G}_{289}^{\circ} / \mathrm{kJmol}^{-1}: & 0 & -601.6 & -110.5 \\\\\mathrm{S}_{298}^{\circ} / \mathrm{JK}^{-1} \mathrm{mol}^{-1}: & 29.9 & 415.5 & 197.6\end{array}$$

Step-by-Step Solution

Answer

The Mond process is thermodynamically feasible with negative ΔG at 80°C for formation and controlled conditions allowing decomposition at 200°C.

Step 1: Calculate the Change in Gibbs Free Energy (ΔG)

First, we use the Gibbs free energy change formula to calculate ΔG for the reaction at 80°C:\[\Delta_{1} G^{\circ} = (\Delta G^{\circ}_{\text{products}}) - (\Delta G^{\circ}_{\text{reactants}}) \]For the reaction: \[\mathrm{Ni(s)} + 4 \mathrm{CO(g)} \rightarrow \mathrm{Ni(CO)_4(g)}\]\[\Delta G^{\circ} = [-601.6] - [0 + 4(-110.5)] = -601.6 + 442 = -159.6 \text{kJ mol}^{-1}\]

Step 2: Calculate the Change in Entropy (ΔS)

Next, calculate the change in entropy for the reaction:\[\Delta S^{\circ} = \Delta S^{\circ}_{\text{products}} - \Delta S^{\circ}_{\text{reactants}} \]\[\Delta S^{\circ} = [415.5] - [29.9 + 4(197.6)] = 415.5 - 820.3 = -404.8 \text{JK}^{-1} \text{mol}^{-1}\]

Step 3: Calculate Gibbs Free Energy Change at 80°C

To check for feasibility at 80°C, use:\[\Delta G = \Delta H - T \Delta S\]We have already found the standard Gibbs free energy for the ideal condition (25°C or 298K), now adjust it for 80°C (353K):\[\Delta G = -159.6 \, kJ/mol - (353 \, K \times (-404.8 \, J/K/mol \times 0.001 \, kJ/J))\]\[\Delta G = -159.6 + 142.8 = -16.8 \, kJ/mol\]This negative ΔG indicates the reaction is thermodynamically feasible at 80°C for forming \(\mathrm{Ni(CO)_4}\).

Step 4: Evaluate Reverse Reaction Feasibility at 200°C

At 200°C, convert the temperature to Kelvin (473K) to analyze the reverse reaction:\[\Delta G' = \Delta H - T \Delta S\]For the reverse process where \(\mathrm{Ni(CO)_4}\) decomposes, use:\[\Delta G' = 159.6 - (473 \, K \times 0.4048) = 159.6 - 191.4 = 31.8 \, kJ/mol\]This positive ΔG for decomposition indicates that at 200°C, the reverse reaction where \(\mathrm{Ni(CO)_4}\) decomposes back into \(\mathrm{Ni(s)}\) and \(\mathrm{CO(g)}\) is endergonic and not spontaneous, but feasible under controlled conditions.

Key Concepts

Thermodynamics

Thermodynamics is a fundamental scientific discipline that explores the flow of energy, principally focusing on the laws dictating energy transformations and interactions in physical systems. In the context of the Mond process, thermodynamics helps us in understanding the energy changes involved in converting nickel into a gaseous compound and then back to its solid form. The first law of thermodynamics, also known as the law of energy conservation, tells us that energy cannot be created or destroyed. Instead, it can only change forms.
The Mond process, therefore, relies heavily on thermodynamic principles to ensure that energy changes occurring at various stages are feasible. This includes analyzing how temperature and pressure differences can drive chemical transformations. These energetic considerations are critical when predicting whether a chemical reaction will occur under specific conditions. By using thermodynamic data like Gibbs free energy and entropy, we can determine the viability of the Mond process for nickel purification.

Gibbs Free Energy

Gibbs free energy is a vital concept in evaluating chemical reaction feasibility. It represents the maximum reversible work a thermodynamic system can perform at a constant temperature and pressure.
The formula for change in Gibbs free energy, \(\Delta G = \Delta H - T \Delta S\), combines enthalpy (\( \Delta H\)) and entropy (\( \Delta S\)) changes. In the Mond process, we used this formula to calculate the \(\Delta G\) for the reaction, indicating the direction of spontaneity at specific temperatures.
A negative \(\Delta G\) value suggests the reaction proceeds spontaneously. For instance, converting nickel and carbon monoxide into \( \mathrm{Ni(CO)_4} \) at 80\( \degree C\) shows a negative \( \Delta G\), confirming feasibility. Conversely, a positive \( \Delta G\) during decomposition at 200\( \degree C\) suggests the reaction isn't spontaneous without the input of additional energy.

Entropy

Entropy is a measure of disorder or randomness in a system, usually denoted as \( \Delta S\). It is a key concept in understanding energy dispersal in physical and chemical processes.
In reactions, entropy change tells us whether a process leads to greater or reduced randomness in the system. When studying the Mond process, calculating the change in entropy helps us understand what happens to the overall disorder of molecules involved.
For the reaction in the Mond process, from solid nickel and carbon monoxide gas to gaseous \( \mathrm{Ni(CO)_4} \), a decrease in entropy indicates a reduction in randomness. This is because fewer gas molecules result, despite the complex \( \mathrm{Ni(CO)_4} \) molecule formed. In thermodynamics, coupling entropy with enthalpy helps predict whether a reaction is feasible at given conditions.

Reaction Feasibility

Reaction feasibility is about evaluating whether a chemical reaction can occur under certain conditions. It is influenced mainly by thermodynamics and encompasses several factors:

• Temperature
• Entropy
• Gibbs Free Energy

Combining these elements, we can determine if a process like the Mond reaction will proceed without external energy.
For instance, in the Mond process, forward and reverse reactions are assessed at different temperatures (\( \text{80\( \degree C\)} \) and \( \text{200\( \degree C\)} \)). At 80\( \degree C\), a negative \( \Delta G\) indicates that forming \( \mathrm{Ni(CO)_4} \) is feasible. On the other hand, decomposing it at 200\( \degree C\) yields a positive \( \Delta G\), suggesting the need for additional energy.
Thus, reaction feasibility studies are essential in industrial applications to optimize conditions for maximum efficiency.