Q.(a)

delta H and delta U for an ideal gas are related by delta H = delta U + delta(n)RT; the reaction quotient Q has the same expression as the equilibrium constant K but can be evaluated at any point in the reaction, not just at equilibrium.

1. Relation between delta H and delta U for an ideal gas: Enthalpy is defined as H = U + PV, where U is internal energy, P is pressure and V is volume. For a change of state (a reaction) at constant temperature: delta H = delta U + delta(PV) For a gaseous system behaving ideally, PV = nRT (the ideal gas equation), so at constant temperature: delta(PV) = delta(nRT) = (delta n) RT where delta n is the change in the number of moles of GASEOUS substances, i.e., (moles of gaseous products) - (moles of gaseous reactants). Substituting this back: delta H = delta U + (delta n) RT This relation lets us convert between the heat change measured at constant volume (which gives delta U directly, since q_v = delta U) and the heat change at constant pressure (which gives delta H directly, since q_p = delta H) for gas-phase reactions, once delta n (the change in moles of gas) is known.
2. Reaction quotient: For a general reaction aA + bB <=> cC + dD, the reaction quotient Qc is defined by the same mathematical expression as the equilibrium constant: Qc = ([C]^c [D]^d) / ([A]^a [B]^b) …