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The thermite reaction is a well-known metal oxidation reaction, which involves the reaction of aluminum (Al) with iron(III) oxide (Fe鈧侽鈧�) to produce aluminum oxide (Al鈧侽鈧�) and iron (Fe). This reaction is commonly used in welding, especially for joining railway tracks due to the intense heat produced.
Balancing the thermite reaction requires ensuring equal numbers of Al, Fe, and O atoms on both sides of the equation. Initially, one aluminum atom reacts with iron(III) oxide, but since we need two aluminum atoms in Al鈧侽鈧� on the product side, we adjust by placing a coefficient of 2 in front of Al.

• This balances the aluminum.
• The iron, which is initially balanced incorrectly with 2 Fe on the left, requires a factor of 2 on Fe to align with the reaction product side.

The balanced equation is:\[2 \mathrm{Al} + \mathrm{Fe}_{2} \mathrm{O}_{3} \rightarrow \mathrm{Al}_{2} \mathrm{O}_{3} + 2 \mathrm{Fe}\]This balance ensures that there are 2 Al, 2 Fe, and 3 O atoms on both sides, maintaining the law of conservation of mass.

Photosynthesis is the critical biochemical process by which green plants, algae, and some bacteria convert light energy into chemical energy, stored in glucose. The general photosynthesis equation is:\[6 \mathrm{CO}_{2} + 6 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} + 6 \mathrm{O}_{2}\]It describes how carbon dioxide (CO鈧�) and water (H鈧侽), in the presence of sunlight, are converted into glucose (C鈧咹鈧佲倐O鈧�) and oxygen (O鈧�). This balanced chemical equation reflects the conservation of atoms:

• 6 carbon atoms on each side from CO鈧� and C鈧咹鈧佲倐O鈧�
• 12 hydrogen atoms from H鈧侽 and C鈧咹鈧佲倐O鈧�
• 18 oxygen atoms contributed by CO鈧�, H鈧侽, and produced as O鈧�

This balance is crucial in illustrating how plants produce glucose, their energy source, and oxygen, a byproduct vital for life on earth.

The gold separation process, also known as gold cyanidation, involves extracting gold from its ore using a solution of sodium cyanide (NaCN). This process involves the chemical reaction between gold (Au), sodium cyanide, oxygen (O鈧�), and water (H鈧侽) to form sodium gold cyanide \(\mathrm{NaAu(CN)}_{2}\) and sodium hydroxide (NaOH).The unbalanced equation is:\[\mathrm{Au} + 2 \mathrm{NaCN} + \mathrm{O}_{2} + \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{NaAu(CN)}_{2} + 3 \mathrm{NaOH}\]Balancing this equation aligns the quantity of each element on both sides:

• Adjust the quantity of sodium: Change to 3 NaCN and 3 NaOH
• Balance oxygen with an extra molecule: Add another H鈧侽 on the left

The balanced equation becomes:\[\mathrm{Au} + 3 \mathrm{NaCN} + \mathrm{O}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{NaAu(CN)}_{2} + 3 \mathrm{NaOH}\]This process efficiently extracts gold by ensuring that the gold atoms are entirely converted into soluble complexes, allowing them to be separated easily from the ore.