CBSE Class 12 Chemistry Chapter 6: General Principles and Processes of Isolation of Elements - NCERT Solutions

Solution: The magnetic separation method is applicable for concentrating ores if either the ore itself or the impurities (gangue) exhibits magnetic properties. This allows for their separation using a magnetic field. Based on common knowledge of ores listed in such tables, iron ores like haematite ($Fe_2O_3$), magnetite ($Fe_3O_4$), siderite ($FeCO_3$), and iron pyrites ($FeS_2$) possess magnetic properties or are associated with magnetic impurities, making them amenable to concentration via magnetic separation.

Solution: In the extraction of aluminium, leaching plays a crucial role in purifying the bauxite ore by concentrating pure alumina ($Al_2O_3$). Bauxite ore often contains impurities such as silica ($SiO_2$), iron oxide ($Fe_2O_3$), and titanium oxide ($TiO_2$). The process involves digesting the powdered bauxite ore with a concentrated solution of sodium hydroxide ($NaOH$) at elevated temperatures (473-523 K) and pressure (35-36 bar). Under these conditions, the amphoteric alumina dissolves to form sodium meta-aluminate, while the acidic silica dissolves as sodium silicate. Basic impurities like iron oxide and titanium oxide remain undissolved.

The relevant chemical reactions are:

$$Al\_2O\_\{3(s)\}\; +\; 2\; NaOH\_\{(aq)\}\; +\; 3\; H\_2O\_\{(l)\}\; \backslash xrightarrow\{473-523\; \backslash text\{\; K\}\}\; 2\; Na[Al(OH)\_4]\_\{(aq)\}$$

Alumina reacts with sodium hydroxide and water to form soluble sodium tetrahydroxoaluminate.

$$SiO\_\{2(s)\}\; +\; 2\; NaOH\_\{(aq)\}\; \backslash xrightarrow\{473-523\; \backslash text\{\; K\}\}\; Na\_2SiO\_\{3(aq)\}\; +\; H\_2O\_\{(l)\}$$

Silica reacts with sodium hydroxide to form soluble sodium silicate.

The insoluble impurities are then filtered off. The filtrate, containing sodium meta-aluminate and sodium silicate, is treated by passing carbon dioxide ($CO_2$) gas. This neutralizes the solution and causes the precipitation of hydrated alumina, while sodium silicate remains in solution.

$$2\; Na[Al(OH)\_4]\_\{(aq)\}\; +\; CO\_\{2(g)\}\; \backslash longrightarrow\; Al\_2O\_3\; \backslash cdot\; xH\_2O\_\{(s)\}\; +\; 2\; NaHCO\_\{3(aq)\}$$

Precipitation is often aided by seeding the solution with a small amount of pre-existing hydrated alumina. The precipitated hydrated alumina is then filtered, washed, dried, and strongly heated (calcined) to obtain pure alumina ($Al_2O_3$).

$$Al\_2O\_3\; \backslash cdot\; xH\_2O\_\{(s)\}\; \backslash xrightarrow\{1470\; \backslash text\{\; K\}\}\; Al\_2O\_\{3(s)\}\; +\; xH\_2O\_\{(g)\}$$

Thus, leaching is essential for separating alumina from its common impurities in the bauxite ore.

Solution: The given reaction, the reduction of chromium(III) oxide ($Cr_2O_3$) by aluminium ($Al$), is thermodynamically feasible because the standard Gibbs free energy change ($\Delta G_0$) is highly negative (-421 kJ). This indicates that the reaction is spontaneous under standard conditions.

However, the reaction does not occur at room temperature primarily because all the reactants ($Cr_2O_3$ and $Al$) and the products ($Al_2O_3$ and $Cr$) are in the solid state at room temperature. For a reaction to proceed, there needs to be an interaction between the reacting species, and in the solid state, the rate of reaction is extremely slow due to limited mobility and contact. Equilibrium between reactants and products is not effectively established at room temperature in the solid phase.

The relationship between Gibbs free energy ($\Delta G$), enthalpy change ($\Delta H$), and entropy change ($\Delta S$) is given by the equation: $\backslash Delta\; G\; =\; \backslash Delta\; H\; -\; T\; \backslash Delta\; S$. While $\Delta G^0$ is negative, indicating feasibility, the activation energy barrier for the reaction in the solid state is very high at room temperature. At higher temperatures, the reactants gain sufficient kinetic energy to overcome this barrier. Furthermore, as temperature increases, the term $T\Delta S$ becomes more significant. If the entropy change ($\Delta S$) is positive (which is often the case when solids react to form products that might have more disorder or if melting occurs), the $-T\Delta S$ term becomes more negative, further decreasing $\Delta G$ and increasing the feasibility of the reaction. When chromium melts at higher temperatures, the reaction proceeds readily, yielding molten chromium.

Solution: Yes, it is true that under certain conditions, magnesium ($Mg$) can reduce silicon dioxide ($SiO_2$), and silicon ($Si$) can reduce magnesium oxide ($MgO$). These reductions are possible due to the relative electrochemical potentials and the conditions under which the reactions are carried out, primarily high temperatures.

1. Mg reducing $SiO_2$:

Magnesium is a highly reactive metal and can reduce silicon dioxide to silicon at elevated temperatures. This reaction is thermodynamically favorable at high temperatures. The condition required is that the reactants must be heated to a sufficiently high temperature, typically above the melting point of magnesium, to allow for effective reaction. The reaction can be represented as:

$2Mg\_\{(l)\}\; +\; SiO\_\{2(l)\}\; \backslash longrightarrow\; 2MgO\_\{(s)\}\; +\; Si\_\{(s)\}$

This process requires high temperatures where both $Mg$ and $SiO_2$ are in a reactive state (e.g., molten).

2. Si reducing MgO:

Conversely, silicon can act as a reducing agent for magnesium oxide ($MgO$) at very high temperatures. This is related to the Ellingham diagram, which shows that at sufficiently high temperatures, the free energy of formation of $SiO_2$ becomes more negative than that of $MgO$, indicating that $Si$ can displace $Mg$ from $MgO$. The condition is again high temperature, where silicon can effectively reduce magnesium oxide. The reaction can be represented as:

$2Si\_\{(s)\}\; +\; 2MgO\_\{(s)\}\; \backslash longrightarrow\; 2Mg\_\{(g)\}\; +\; SiO\_\{2(s)\}$

In summary, both reactions are possible but require specific high-temperature conditions where the thermodynamic stability of the oxides shifts, allowing for the reduction to occur.