Question

Impure nickel, refined by smelting sulfide ores in a blast furnace, can be converted into metal from \(99.90 \%\) to \(99.99 \%\) purity by the Mond process. The primary reaction involved in the Mond process is $$\mathrm{Ni}(s)+4 \mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(\mathrm{CO})_{4}(g)$$ a. Without referring to Appendix 4, predict the sign of \(\Delta S^{\circ}\) for the above reaction. Explain. b. The spontaneity of the above reaction is temperature dependent. Predict the sign of \(\Delta S_{\text {sarr }}\) for this reaction. Explain. c. For \(\mathrm{Ni}(\mathrm{CO})_{4}(g), \Delta H_{\mathrm{f}}^{\circ}=-607 \mathrm{~kJ} / \mathrm{mol}\) and \(S^{\circ}=417 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\) at \(298 \mathrm{~K}\). Using these values and data in Appendix 4, calculate \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for the above reaction. d. Calculate the temperature at which \(\Delta G^{\circ}=0(K=1)\) for the above reaction, assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature. e. The first step of the Mond process involves equilibrating impure nickel with \(\mathrm{CO}(\mathrm{g})\) and \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) at about \(50^{\circ} \mathrm{C}\). The purpose of this step is to convert as much nickel as possible into the gas phase. Calculate the equilibrium constant for the preceding reaction at \(50 .{ }^{\circ} \mathrm{C}\). f. In the second step of the Mond process, the gaseous \(\mathrm{Ni}(\mathrm{CO})_{4}\) is isolated and heated to \(227^{\circ} \mathrm{C}\). The purpose of this step is to deposit as much nickel as possible as pure solid (the reverse of the preceding reaction). Calculate the equilibrium constant for the preceding reaction at \(227^{\circ} \mathrm{C}\). g. Why is temperature increased for the second step of the Mond process? h. The Mond process relies on the volatility of \(\mathrm{Ni}(\mathrm{CO})_{4}\) for its success. Only pressures and temperatures at which \(\mathrm{Ni}(\mathrm{CO})_{4}\) is a gas are useful. A recently developed variation of the Mond process carries out the first step at higher pressures and a temperature of \(152^{\circ} \mathrm{C}\). Estimate the maximum pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) that can be attained before the gas will liquefy at \(152^{\circ} \mathrm{C}\). The boiling point for \(\mathrm{Ni}(\mathrm{CO})_{4}\) is \(42^{\circ} \mathrm{C}\) and the enthalpy of vaporization is \(29.0 \mathrm{~kJ} / \mathrm{mol}\).

Short answer

The sign of \(\Delta S^\circ\) will be negative due to the stoichiometry of the reaction. The sign of \(\Delta S_\text{sarr}\) will also be negative. Using the given values and Appendix 4 data, the calculated values of \(\Delta H^\circ\) and \(\Delta S^\circ\) can be obtained. Temperature at which \(\Delta G^\circ = 0\) can be found using the Gibbs-Helmholtz equation. Equilibrium constants at \(50^{\circ} \mathrm{C}\) and \(227^{\circ} \mathrm{C}\) can be calculated using the Van't Hoff equation. The increased temperature in the second step of Mond process shifts the reaction towards the reverse direction, favoring the deposition of solid nickel. Finally, the maximum pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) at \(152^{\circ} \mathrm{C}\) before it will liquefy can be estimated using the Clausius-Clapeyron equation.

Step-by-step solution

(a. Predicting sign of ΔS°)

In order to predict the sign of \(\Delta S^\circ\), we can analyze the stoichiometry of the gaseous species involved in the reaction. The change in entropy is related to the disorder of the system. Going from one solid and four gaseous molecules to one gaseous molecule, the system becomes more ordered; therefore, we expect that the change in entropy, \(\Delta S^\circ\), will be negative.

(b. Predicting sign of ΔSsarr)

The spontaneity of the reaction is temperature dependent, so we use the Gibbs-Helmholtz equation: $$\Delta G^\circ = \Delta H^\circ - T \Delta S^\circ$$ Given that the reaction should spontaneously convert at lower temperatures and spontaneous positon at higher temperatures, the sign of \(\Delta G^\circ\) should change from negative to positive as the temperature increases. Thus, \(\Delta H^\circ\) must be positive and \(\Delta S^\circ\) must be negative, as predicted in part (a). Hence, the sign of \(\Delta S_\text{sarr}\) should be negative.

(c. Calculating ΔH° and ΔS°)

Using the given data for \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) and Appendix 4 for the values of \(\mathrm{Ni}(s)\) and \(\mathrm{CO}(g)\), we can calculate \(\Delta H^\circ\) and \(\Delta S^\circ\): $$\Delta H^\circ = \Delta H_{\mathrm{f}}^{\circ}(\mathrm{Ni}(\mathrm{CO})_{4}(g)) - [\Delta H_{\mathrm{f}}^{\circ}(\mathrm{Ni}(s)) + 4 \Delta H_{\mathrm{f}}^{\circ}(\mathrm{CO}(g))]$$ $$\Delta S^\circ = S^{\circ}(\mathrm{Ni}(\mathrm{CO})_{4}(g)) - [S^{\circ}(\mathrm{Ni}(s)) + 4S^{\circ}(\mathrm{CO}(g))]$$ Plug in the values and calculate the ΔH° and ΔS°.

(d. Temperature at ΔG° = 0)

We know that at equilibrium, \(\Delta G^\circ = 0\), so from the Gibbs-Helmholtz equation: $$0 = \Delta H^\circ - T \Delta S^\circ \Rightarrow T = \frac{\Delta H^\circ}{\Delta S^\circ}$$ Plug in the calculated values of \(\Delta H^\circ\) and \(\Delta S^\circ\) to find the temperature at which \(\Delta G^\circ = 0\).

(e. Equilibrium constant at 50°C)

To calculate the equilibrium constant at \(50^{\circ} \mathrm{C}\), we use the Van't Hoff equation: $$\ln K = -\frac{\Delta H^\circ}{RT} + \frac{\Delta S^\circ}{R}$$ Plug in the values of \(\Delta H^\circ\), \(\Delta S^\circ\) and the temperature converted to Kelvin, and then calculate K.

(f. Equilibrium constant at 227°C)

Repeat the same process as in part (e) but this time at \(227^{\circ} \mathrm{C}\) to calculate the equilibrium constant, K.

(g. Importance of increased temperature)

The temperature is increased during the second step of the Mond process to shift the reaction towards the reverse direction, which means the formation of solid nickel. From the Van't Hoff equation, we know that an increase in temperature will lead to a decrease in K, causing the reaction to shift towards the reactant side, which favors the deposition of solid nickel.

(h. Estimating maximum pressure)

To estimate the maximum pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) at \(152^{\circ} \mathrm{C}\) before it will liquefy, we can use the Clausius-Clapeyron equation: $$\ln \frac{P_2}{P_1} = \frac{\Delta H_\text{vap}}{R} \left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$ Given the boiling point and the enthalpy of vaporization, we can solve for the pressure, \(P_2\), and estimate the maximum pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}(g)\) before it will liquefy.

Key concepts

Entropy Change

The concept of entropy change, \(\Delta S\), describes the degree of disorder or randomness in a system during a reaction. For the Mond process reaction \(\text{Ni}(s) + 4 \text{CO}(g) \rightleftharpoons \text{Ni(CO)}_4(g)\), we observe a transition from one solid atom and four gaseous molecules to a single gaseous molecule, nickel carbonyl. This results in decreased entropy.

In other words, by mathematically analyzing the reaction, \(\Delta S\) is expected to be negative because there are fewer gaseous molecules creating a less disordered state. The negative sign of \(\Delta S\) indicates that the system is becoming more ordered. This physical change in the system's molecular arrangement influences the spontaneity and equilibrium of reactions. Entropy is a key component of the Gibbs Free Energy equation that determines reaction spontaneity.

Gibbs Free Energy

Gibbs Free Energy, \(\Delta G\), is a crucial thermodynamic potential used to predict reaction spontaneity. In the Mond process, the equation is given by: \[\Delta G = \Delta H - T\Delta S\] where \(\Delta H\) is the change in enthalpy, \(T\) is the temperature in Kelvin, and \(\Delta S\) is the change in entropy.

If \(\Delta G\) is negative, the reaction is spontaneous under the given conditions. Conversely, a positive \(\Delta G\) indicates a non-spontaneous reaction without external influence. For the production of nickel carbonyl, the reaction's spontaneity at different temperatures is assessed using \(\Delta G\). Since the process relies on temperature variations to drive the change in nickel purity, understanding how temperature affects \(\Delta G\) helps in optimizing the conditions for purification. \(\Delta G=0\) at equilibrium conditions, equating temperature with \(\frac{\Delta H}{\Delta S}\), determines the specific point where the reaction ceases to progress further in either direction.

Equilibrium Constant

The equilibrium constant, \(K\), is a measure that indicates the extent to which a reaction proceeds. It is directly related to Gibbs Free Energy as \[\Delta G^\circ = -RT \ln(K)\] where \(R\) is the universal gas constant and \(T\) is the temperature in Kelvin. This equation shows how both thermodynamic properties are interdependent in quantifying reaction progress.

At \(K=1\), the system is at equilibrium, meaning the forward and reverse reactions occur at equal rates. By computing \(K\) at specific temperatures during the Mond process, one can identify how efficiently nickel converts to its gaseous form and back to solid, helping optimize the purification process. When \(K>1\), the reaction favors product formation, and when \(K<1\), it favors the reactants, giving insights into which direction the reaction naturally inclines at given temperatures.

Reaction Spontaneity

Reaction spontaneity describes whether a given chemical reaction will proceed by itself without needing continuous input of energy. It depends primarily on the sign and magnitude of Gibbs Free Energy, \(\Delta G\). For the Mond process, the spontaneity heavily influences operational efficiency.

At lower temperatures, the Mond process is guided in such a way that forming gaseous nickel carbonyl is more favorable since \(\Delta G\) is negative. As the system progresses towards higher temperatures, \(\Delta G\) changes due to the balance between enthalpy and entropy. The process is designed to exploit these shifts in spontaneity to either capture nickel in its gaseous state or solid-state through successive temperature manipulations, making the spontaneity concept foundational for this industrial application.