The change in internal energy (ΔU) represents the total change in energy contained within the system. It is the sum of all possible forms of energy (kinetic and potential) of the molecules, atoms, and subatomic particles within the system. It is a state function, depending only on the initial and final states.

Enthalpy (H) is defined as H = U + PV. It is a state function. Enthalpy was introduced to conveniently handle energy changes for processes occurring at constant pressure, which is a common condition in chemical reactions. The change in enthalpy (ΔH) directly gives the heat exchanged (qₚ) at constant pressure.

The relationship is ΔH = ΔU + Δ(PV). At constant pressure, this simplifies to ΔH = ΔU + PΔV where ΔH is the change in Enthalpy, ΔU is the change in Internal Energy, and PΔV represents the pressure-volume work done by or on the system.

ΔH is equal to the heat absorbed or released (qₚ) only when the process is carried out at constant pressure. This is because, by definition, ΔH = qₚ.

In a sealed, rigid container, the volume is constant (ΔV = 0). Therefore, no pressure-volume work (PΔV) is done. According to the first law of thermodynamics (ΔU = q + w), and with w = -PΔV = 0, it follows that ΔU = qᵥ. The heat exchanged at constant volume equals the change in internal energy.

A bomb calorimeter has a strong, sealed container (the bomb) that does not allow any change in volume during the combustion reaction. Therefore, it is a constant-volume apparatus. It directly measures the heat change at constant volume (qᵥ), which is equal to the change in internal energy, ΔU.

An open beaker is exposed to the atmosphere, so the pressure remains constant (atmospheric pressure). It is a constant-pressure process. In this setup, the heat change at constant pressure (qₚ) is measured, which is equal to the change in enthalpy, ΔH.

The relationship is ΔH = ΔU + Δn(g)RT, where Δn(g) is the change in the number of moles of gaseous products and reactants, R is the universal gas constant, and T is the absolute temperature at which the reaction occurs.

The magnitude of ΔH will be greater than that of ΔU. Calculate Δn(g) = (0) – (1 + 0.5) = -1.5. Using ΔH = ΔU + Δn(g)RT, the term Δn(g)RT is negative. Therefore, ΔH is a larger negative number than ΔU, meaning its magnitude is greater.

A coffee-cup calorimeter is designed to be a constant-pressure device. The measured heat (q) is qₚ, which is equal to ΔH. The work done in expansion is automatically accounted for in the definition of ΔH.

This implies the reaction is highly exothermic at constant pressure, but the internal energy change is small. Using ΔH = ΔU + PΔV, for ΔH to be much more negative than ΔU, the PΔV term must be negative. This typically happens when there is a large increase in the number of moles of gas (Δn(g) > 0).

For solids and liquids, the volume change (ΔV) during a reaction is very small. Since ΔH = ΔU + PΔV, and PΔV is negligible, it follows that ΔH ≈ ΔU.

While ΔH is positive (unfavorable for spontaneity), the reaction leads to a large increase in disorder (entropy, ΔS) because one solid mole decomposes into two gaseous moles. The increase in entropy can drive the reaction to be spontaneous, as governed by ΔG = ΔH – TΔS.

Δn(g) = 2 – (1+3) = -2. A negative Δn(g) means the total volume decreases (ΔV is negative). Therefore, work done by the system, w = -PΔV, will be positive (because ΔV is negative, -PΔV becomes positive).

For any cyclic process (where the system returns to its initial state), both ΔU and ΔH are zero. This is because U and H are state functions. Since the initial and final states are identical, the net change is zero.

When ice melts, it expands (volume increases). The system (ice/water) is doing work by pushing back the atmosphere. Therefore, work is done by the system (w is negative according to the IUPAC sign convention).

For an ideal gas, the internal energy (U) depends only on temperature. In an isothermal process, temperature is constant, so ΔU = 0. From the first law, ΔU = q + w, therefore 0 = q + w, which implies q = -w.

Enthalpy is a relative measure of energy. We need a reference point. The formation reaction of an element from itself is not a real chemical change. By convention, setting this value to zero for all stable elements provides a consistent baseline from which the enthalpies of formation of compounds can be measured.

Yes, this statement is true. Enthalpy (H) is a state function. The enthalpy difference between two states (reactants and products) is fixed. If the forward reaction has ΔH = +x kJ, then the reverse reaction must have ΔH = -x kJ.

ΔH is greater than ΔU. Vaporization involves a large increase in volume (ΔV > 0) as liquid turns to gas. Therefore, the PΔV term in ΔH = ΔU + PΔV is positive. Adding a positive quantity to ΔU results in ΔH being greater than ΔU.