Thermodynamics

ΔH = ΔU + Δn_g RT

Step 1: We know ΔH = ΔU + pΔV at constant pressure. Step 2: For gases, using ideal gas law: pΔV = Δn_g RT, where Δn_g = moles of gaseous products − moles of gaseous reactants. Step 3: Substituting: ΔH = ΔU + Δn_g RT. Step 4: This equation is very useful — if Δn_g = 0 (equal moles of gas on both sides), then ΔH = ΔU. If Δn_g > 0 (more moles of gas produced), ΔH > ΔU. Step 5: The option ΔH = ΔU − Δn_g RT is incorrect as the sign is wrong. The other two options mix up variables incorrectly.

Heat change at constant volume (ΔU)

Step 1: A bomb calorimeter consists of a strong sealed steel vessel (the bomb) immersed in a water bath. Step 2: Since the bomb is sealed and rigid, its volume cannot change — it operates at constant volume (ΔV = 0). Step 3: At constant volume, no pressure-volume work is done (w = 0), so ΔU = q_V — the heat measured equals the change in internal energy. Step 4: The heat released by the reaction warms the surrounding water, and by measuring the temperature rise, we can calculate q_V = C_V × ΔT. Step 5: To measure ΔH at constant pressure, we use a simple open calorimeter. Entropy and Gibbs energ

Is the same whether the reaction occurs in one step or multiple steps

Step 1: Hess's Law is a direct consequence of enthalpy being a state function — meaning ΔH depends only on initial and final states, not on the path taken. Step 2: Hess's Law states: if a reaction takes place in several steps, the standard reaction enthalpy equals the sum of enthalpies of all intermediate steps. Step 3: This is extremely useful for reactions where direct measurement is impossible. For example, C(s) + ½O₂(g) → CO(g) cannot be measured directly, but can be calculated using enthalpies of other reactions. Step 4: Hess's Law allows us to add, subtract, or reverse thermochemical equ

Zero

Step 1: Standard enthalpy of formation is defined as the enthalpy change when one mole of a compound is formed from its elements in their most stable reference states at 298 K and 1 bar. Step 2: By convention, elements in their most stable reference state are assigned Δ_f H° = 0. Step 3: Examples of reference states: H₂(g), O₂(g), C(graphite), S(rhombic), Na(s), Fe(s) — all have Δ_f H° = 0. Step 4: This makes logical sense — forming an element from itself involves no chemical change, so no enthalpy change occurs. Step 5: Any non-zero value would be incorrect. This convention helps us calculate