CBSE Class 12 Chemistry Chapter 11: General Principles and Processes of Isolation of Elements - NCERT Solutions

Solution: The magnetic separation method is employed when either the ore or the undesired rocky material (gangue) possesses magnetic properties. This allows for their separation using a magnetic field. Based on the typical composition of ores mentioned in metallurgical contexts (like Table 6.1 often includes), iron ores such as haematite ($Fe\_2O\_3$), magnetite ($Fe\_3O\_4$), and siderite ($FeCO\_3$) can be concentrated using magnetic separation because they are attracted to a magnet. Iron pyrites ($FeS\_2$) may also exhibit some magnetic properties or be separated if the gangue is non-magnetic.

Solution: In the extraction of aluminium, leaching plays a crucial role in purifying the bauxite ore. Bauxite ore often contains impurities like silica ($SiO\_2$), iron oxides, and titanium dioxide. The significance of leaching lies in its ability to selectively dissolve the valuable component, alumina ($Al\_2O\_3$), while leaving behind many impurities. This is typically achieved by digesting the powdered ore with a concentrated solution of sodium hydroxide ($NaOH$) at elevated temperatures (473-523 K) and pressure (35-36 bar). During this process, alumina dissolves to form soluble sodium meta-aluminate, whereas silica reacts to form soluble sodium silicate, and iron oxides remain undissolved.

The relevant 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 $NaOH$ and water to form sodium tetrahydroxoaluminate.

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

Silica reacts with $NaOH$ to form sodium silicate.

The insoluble impurities are then filtered off. Subsequently, the solution containing sodium meta-aluminate is treated with carbon dioxide ($CO\_2$) gas, which causes the precipitation of hydrated alumina. Sodium silicate remains in the solution.

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

The precipitated hydrated alumina is then filtered, dried, and heated strongly 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 a critical step for concentrating alumina from the crude bauxite ore.

Solution: The given reaction, the reduction of chromium(III) oxide ($Cr\_2O\_3$) by aluminium ($Al$), is thermodynamically feasible at standard conditions because the change in Gibbs free energy ($\backslash Delta\; G\_0$) is highly negative (-421 kJ). This indicates that the forward reaction is spontaneous from a thermodynamic perspective.

However, the reaction does not occur at room temperature primarily because both 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 sufficient contact and mobility between the reacting species. In the solid state, the atoms or molecules have limited movement, and the reaction rate is extremely slow, effectively making it non-existent at room temperature. The activation energy barrier for the reaction between solids is also very high.

The feasibility of a reaction is also described by the Gibbs energy equation: $\backslash Delta\; G\; =\; \backslash Delta\; H\; -\; T\; \backslash Delta\; S$. While $\backslash Delta\; G\_0$ is negative, the reaction requires a significant amount of energy to initiate, especially at lower temperatures. At higher temperatures, the reactants may melt or vaporize, increasing their mobility and allowing the reaction to proceed at a significant rate. Furthermore, as temperature increases, the $T\; \backslash Delta\; S$ term becomes more significant. If $\backslash Delta\; S$ is positive (as is often the case when solids form a more dispersed product or when melting occurs), increasing temperature makes $\backslash Delta\; G$ even more negative, further enhancing the feasibility.

Solution: Yes, it is true that under certain conditions, magnesium ($Mg$) can reduce silicon dioxide ($SiO\_2$), and silicon ($Si$) can reduce magnesium oxide ($MgO$). The feasibility of these reactions depends on the relative thermodynamic stability of the metal oxides, which can be predicted using Ellingham diagrams or by considering the Gibbs free energy changes at different temperatures.

1. Mg reducing $SiO\_2$:

Magnesium is a highly reactive metal and a strong reducing agent. At sufficiently high temperatures, magnesium can reduce silicon dioxide to elemental silicon. The reaction is:

$$2\; Mg\_\{(s)\}\; +\; SiO\_\{2(s)\}\; \backslash xrightarrow\{\backslash text\{High\; Temp.\}\}\; 2\; MgO\_\{(s)\}\; +\; Si\_\{(s)\}$$

This reaction is thermodynamically favorable at high temperatures because the formation of magnesium oxide ($MgO$) is more stable than the formation of silicon dioxide ($SiO\_2$) under these conditions. The high temperature provides the necessary energy for the reaction to occur and overcome any activation barriers.

2. Si reducing $MgO$:

Silicon, while less reactive than magnesium, can act as a reducing agent for magnesium oxide at very high temperatures. The reaction is:

$$2\; Si\_\{(s)\}\; +\; 3\; MgO\_\{(s)\}\; \backslash xrightarrow\{\backslash text\{Very\; High\; Temp.\}\}\; 2\; Mg\_\{(g)\}\; +\; SiO\_\{2(s)\}$$

This reaction becomes feasible at very high temperatures where the Gibbs free energy change becomes negative. At these extreme temperatures, magnesium metal is produced as a gas, and silicon dioxide is formed. The condition is that the temperature must be high enough for the reduction of $MgO$ by $Si$ to be thermodynamically favorable, which is typically a higher temperature than required for Mg to reduce $SiO\_2$.

In summary, the conditions required are high temperatures, where the relative thermodynamic stability of the oxides dictates which metal can act as a reducing agent for the oxide of the other.