Energy Changes in Chemical Reactions

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Internal Energy

Every substance possesses a definite quantity of energy, under a given set of factors such as chemical nature of the substance, temperature and pressure. The total energy contained in a system or substance is called its internal energy or intrinsic energy. It is represented by the symbol 'E' or 'U'. Stated differently, it is the sum of different forms of energies found in the components of the system such as:

• Translational kinetic energy of atoms or molecules E_t.

• Rotational energy of atoms or molecules E_r.

• Vibrational energy of atoms or molecules E_v.

• Electronic energy (sum of energies in the occupied orbitals E_e)_.

• Inter-molecular interaction energy of the constituent particles of the system V_T.

• Bond nuclear energy E_b, etc.

Different substances have different internal energies depending upon the nature of the constituting atoms, bonds and other conditions of the system temperature, pressure, etc. The internal energy of 1 mole of carbon dioxide will be different from the internal energy of 1mole of sulphur dioxide even under similar conditions of temperature and pressure. Further the internal energy of 1 mole of water at 300 K is different than that of one mole of water at 310 K under same atmospheric pressure.

Internal Energy Change

The internal energy of a system depends upon the state of the system and not on how the system reached the state. The absolute value of internal energy possessed by a substance or system cannot be calculated because it is not possible to find the accurate values of different types of energies, such as translational, vibrational, rotational, chemical energy, etc. stored in a system. However, the change in the internal energy depends only upon the initial and final state of the change and not on how it was brought about.

Thus, the change in the internal energy of a reaction may be considered as the difference between the internal energies of the products and the reactants.

DE = E_products - E_reactants = E_p - E_r

where, E_p is the internal energy of the products, E_r is internal energy of the reactants and DE gives the change in internal energy.

If the internal energy of the products is less than the internal energy of the reactants, then DE would be negative.

DE = E_p - E_r = -ve (Ep < Er)

If the internal energy of the products is more than the internal energy of the reactants, the DE would be positive.

DE = E_p - E_r = +ve (Ep > Er)

If a reaction is carried out at constant temperature and constant volume then no work is done and the heat exchanged with the surroundings is equal to change in internal energy.

Thus, the change in internal energy (DE) of a reaction is:

DE = Heat absorbed or evolved in a reaction at constant temperature and volume.

The change in internal energy in a chemical reaction is measured with the help of an apparatus known as bomb calorimeter.

Problems

2. A system absorbs 470 J of heat and does work equivalent to 200J on its surroundings. Calculate the change in internal energy.

Solution

Heat absorbed by the system = 470 J or q = 470 J

Work done by the system = 200 J or w = - 200 J

According to first law of thermodynamics

DE = q + w

DE = 470 - 200 = 270 J

3. A gas absorbs 120 J of heat and expands against the external pressure of 1.10atm from a volume of 0.5L to 2.0L. What is the change in internal energy? (1L atm = 101.3J)

Solution

Work of expansion, w = PDV

DV = 2.0 - 0.5 =1.5L, P = 836 mm of Hg

PDV = 1.10 x 1.5

= 1.650 L atm

= 1.650 x 101.3 (1L atm = 101.3 J)

= 167.1 J

Since work is done by the system w = - 167.1 J

Heat absorbed by the system = 120J or q = + 120J

Now, DE = q + w

= 120 J + (-167.1) = - 47.1 J