Question: What is hybridization? Explain sp³ hybridization in methane.

Solution: Hybridization is the mixing of atomic orbitals to form new hybrid orbitals. In methane (CH₄), carbon undergoes sp³ hybridization, where one 2s orbital and three 2p orbitals combine to form four sp³ hybrid orbitals. These orbitals are arranged tetrahedrally, with a bond angle of 109.5°.

Question: State the first law of thermodynamics and explain its application.

Solution: The first law of thermodynamics states that energy cannot be created or destroyed, only transformed. Mathematically, it is expressed as: \[ \Delta U = q – W \] This law is used to analyze energy changes in chemical reactions and physical processes.

Question: Derive the ideal gas equation.

Solution: The ideal gas equation is derived by combining Boyle’s law, Charles’s law, and Avogadro’s law. The final equation is: \[ PV = nRT \] Where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the universal gas constant, and \( T \) is temperature.