Internal Energy & Enthalpy
Decode the heat content of chemical reactions. Master the difference between constant volume and constant pressure heat, the critical $\Delta n_g RT$ relation, and Heat Capacity.
Module Focus
Most chemical reactions are carried out in open vessels (like test tubes or beakers) under a constant atmospheric pressure. Because the system can expand or contract, some energy is lost or gained as P-V work. To accurately track the total heat content of such systems, we must distinguish between Internal Energy ($U$) and Enthalpy ($H$). Misunderstanding when to use $\Delta H$ versus $\Delta U$ is the #1 cause of numerical errors in Thermodynamics.
1. Internal Energy ($U$ or $E$)
Internal Energy is the sum of all possible kinds of energies (translational, rotational, vibrational, electronic, nuclear) present in a system.
- It is an Extensive Property (depends on the amount of substance).
- It is a State Function (depends only on initial and final states, not the path).
- The absolute value of $U$ cannot be measured. We can only measure the change: $\Delta U = U_{\text{final}} - U_{\text{initial}}$.
- For an ideal gas, internal energy depends only on Temperature. If $\Delta T = 0$ (Isothermal), then $\Delta U = 0$.
If a process takes place in a closed, rigid container, volume is constant ($\Delta V = 0$). Work done ($w = -P\Delta V$) is zero.
From the First Law ($\Delta U = q + w$), substituting $w=0$ gives:
Measured experimentally using a Bomb Calorimeter.
2. Enthalpy ($H$)
Enthalpy is the total heat content of a system at constant pressure. It accounts for both the internal energy of the system and the energy required to make room for it by displacing its environment (P-V work).
Mathematical Definition
Like Internal Energy, Enthalpy is an extensive property and a state function. We can only measure its change ($\Delta H$).
Heat at Constant Pressure ($q_p$)
For a process at constant pressure (like open-beaker reactions), the change in enthalpy is given by: $\Delta H = \Delta U + P\Delta V$.
Since $\Delta U = q_p + w$ and $w = -P\Delta V$, substituting these gives:
Therefore, the heat absorbed or released in an open vessel is exactly equal to the change in Enthalpy.
3. The Critical Relationship: $\Delta H$ vs $\Delta U$
For reactions involving gases, the volume changes significantly. Assuming ideal gas behavior ($PV = nRT$), we can substitute $P\Delta V$ with $\Delta n_g RT$.
$\Delta n_g = (\text{Sum of moles of gaseous products}) - (\text{Sum of moles of gaseous reactants})$
Example 1: $H_2(g) + I_2(g) \rightarrow 2HI(g)$
$\Delta n_g = 2 - (1 + 1) = 0 \implies \mathbf{\Delta H = \Delta U}$
Example 2: $C(s) + O_2(g) \rightarrow CO_2(g)$
$\Delta n_g = 1 - 1 = 0 \implies \mathbf{\Delta H = \Delta U}$ *(Carbon is solid!)*
Example 3: $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$
$\Delta n_g = 2 - 4 = -2 \implies \mathbf{\Delta H < \Delta U}$
Unit Note: Always use $R = 8.314 \text{ J K}^{-1} \text{mol}^{-1}$ and ensure $\Delta U$ is in Joules (not kJ) before adding!
4. Heat Capacity ($C$)
Heat capacity is the amount of heat required to raise the temperature of a system by $1^\circ C$ or $1 \text{ K}$.
$\mathbf{\Delta H = n \cdot C_p \cdot \Delta T}$
$\mathbf{\Delta U = n \cdot C_v \cdot \Delta T}$
For 1 mole of an ideal gas, expanding at constant pressure requires extra energy to do work against the atmosphere. Therefore, $C_p$ is always greater than $C_v$.
(Where $R$ is the universal gas constant)
NEET Grand Test: Enthalpy & $\Delta U$
15 High-Order Thinking Questions testing $\Delta n_g$ traps, bomb calorimetry, and unit conversions.
Join the Ultimate Chemistry Crash Course
Master Chemical Thermodynamics. Get access to our full suite of Rapid Revision modules, formula sheets, and mock tests specifically designed for the NTA NEET pattern.
Explore All NEET Modules →
No comments:
Post a Comment