Question

In the Mond process for the purification of nickel, \(\mathrm{CO}\) is passed over metallic nickel to give \(\mathrm{Ni}(\mathrm{CO})_{4}\) : $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftarrows \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ Given that the standard free energies of formation of \(\mathrm{CO}(g)\) and \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) are -137.3 and \(-587.4 \mathrm{~kJ} / \mathrm{mol}\) respectively, calculate the equilibrium constant of the reaction at \(80^{\circ} \mathrm{C}\). (Assume \(\Delta G_{\mathrm{f}}^{\circ}\) to be independent of temperature.)

Short answer

The equilibrium constant, K, is approximately 448,000 at 80°C.

Step-by-step solution

Calculate ΔG° for Reaction

To find the ΔG° for the reaction, use the equation for the change in Gibbs free energy: \[ \Delta G^{\circ}_{reaction} = \sum \Delta G^{\circ}_{f, \text{products}} - \sum \Delta G^{\circ}_{f, \text{reactants}} \]Since the only product is \( \mathrm{Ni}(\mathrm{CO})_{4}(g) \) and the reactants are \( \mathrm{Ni}(s) \) and 4 \( \mathrm{CO}(g) \), with \( \Delta G^{\circ}_{f, \text{Ni}} = 0 \) (because it is in its standard state), the equation becomes:\[ \Delta G^{\circ}_{reaction} = (-587.4 \, \text{kJ/mol}) - 4(-137.3 \, \text{kJ/mol}) \]This calculates to:\[ \Delta G^{\circ}_{reaction} = -587.4 + 549.2 = -38.2 \, \text{kJ/mol} \]

Convert Temperature to Kelvin

The reaction temperature is given as \(80^{\circ} \text{C}\). Convert this into Kelvin using the formula:\[ T(K) = T(\degree C) + 273.15 \]Substitute 80 into the formula:\[ T = 80 + 273.15 = 353.15 \text{ K} \]

Calculate Equilibrium Constant (K) Using ΔG°

Gibbs free energy change is related to the equilibrium constant by the equation:\[ \Delta G^{\circ} = -RT \ln K \]where \( R \) is the universal gas constant, \( R = 8.314 \, \text{J/mol K} \).First, convert \( \Delta G^{\circ} \) from \( \text{kJ/mol} \) to \( \text{J/mol} \):\[ \Delta G^{\circ}_{reaction} = -38.2 \, \text{kJ/mol} \times 1000 \, \frac{\text{J}}{\text{kJ}} = -38200 \, \text{J/mol} \]Solve for \( K \):\[ -38200 = -(8.314)(353.15) \ln K \]Simplify and solve for \( \ln K \):\[ \ln K = \frac{-38200}{-2934.361} \approx 13.018 \]Solve for \( K \):\[ K = e^{13.018} \approx 448000 \]

Key concepts

Mond process

The Mond process is a method for purifying nickel. This process relies on the unique properties of carbon monoxide (\(\mathrm{CO}\)), which reacts with nickel to form nickel tetracarbonyl (\(\mathrm{Ni}(\mathrm{CO})_{4}\)). This reaction occurs when carbon monoxide is passed over impure nickel at moderate temperatures. The reaction converts solid nickel into a volatile compound, \(\mathrm{Ni}(\mathrm{CO})_{4}\).

• Metallic nickel (solid) and carbon monoxide gas form nickel tetracarbonyl gas.
• This transformation occurs because nickel tetracarbonyl is both volatile and thermally stable.

At slightly higher temperatures, nickel tetracarbonyl decomposes, releasing pure nickel and carbon monoxide. This process not only purifies nickel but also leverages recycling of carbon monoxide, making it efficient.

Gibbs free energy

Gibbs free energy, or \(\Delta G\), is a thermodynamic quantity that helps predict whether a reaction will occur spontaneously. To assess a reaction's spontaneity, consider the sign of \(\Delta G\):

• If \(\Delta G\) is negative, the process can proceed spontaneously.
• If \(\Delta G\) is zero, the system is in equilibrium, no net change occurs.
• If \(\Delta G\) is positive, the reaction is non-spontaneous under standard conditions.

In the context of the Mond process, the calculation of \(\Delta G^{\circ}\) of the reaction provides insight into the potential spontaneity of nickel purification:\[\Delta G^{\circ}_{reaction} = \sum \Delta G^{\circ}_{f, \text{products}} - \sum \Delta G^{\circ}_{f, \text{reactants}}\]Thus, a negative \(\Delta G^{\circ}\) indicates favorable conditions for purifying nickel.

standard free energy of formation

The standard free energy of formation (\(\Delta G^{\circ}_{f}\)) measures the free energy change when one mole of a compound forms from its elements in their standard states. This value is crucial for calculating a reaction's \(\Delta G^{\circ}\). In any reaction, comparing the free energy of products and reactants helps in assessing the feasibility and extent.

• The standard free energy of formation for carbon monoxide is given as \(-137.3 \, \text{kJ/mol}\).
• The standard free energy of formation for nickel tetracarbonyl is \(-587.4 \, \text{kJ/mol}\).

When purifying nickel through the Mond process, we calculate the total Gibbs free energy change. This calculation uses these \(\Delta G^{\circ}_{f}\) values in the following manner:\[\Delta G^{\circ}_{reaction} = (\Delta G^{\circ}_{f, \text{products}}) - (\Delta G^{\circ}_{f, \text{reactants}})\]

nickel purification

Nickel purification is vital for obtaining high-quality nickel for industrial applications. The Mond process plays a key role in achieving this by transforming nickel into nickel tetracarbonyl and back again.This purification method operates over several steps:

• Initial reaction of impure nickel with carbon monoxide to form nickel tetracarbonyl (\(\mathrm{Ni}(\mathrm{CO})_{4}\)).
• Decomposition of the nickel tetracarbonyl at higher temperatures back into pure nickel and carbon monoxide.

Through these steps, particularly the decomposition phase, impurities are separated out, leaving behind refined nickel. The overall design of this process ensures efficiency and sustainability by reusing carbon monoxide, making it an environmentally friendly choice for nickel purification.