Question

Correct mathematical formulation of first law of thermodynamics used in thermochemistry is:
A)\[\Delta H=\Delta U+\Delta nRT\]
B) \[\Delta U=\Delta H+\Delta nRT\]
C) \[\Delta H=\Delta U-\Delta nRT\]
D) \[\Delta H=-\Delta U+\Delta nRT\]

Answer 1

Hint: The answer for this question includes the fact that the enthalpy of a system is a negative value and to get that negative value the R.H.S term should be in form that the answer will be a negative one.

Complete step by step answer:
From the lower classes of chemistry we have learnt about the thermodynamics of the system and surroundings which is referred to heat and energy and called as chemical thermodynamics.
- Chemical thermodynamics is the study of heat and the work done by the system or surroundings which basically confines it to the laws of thermodynamics.
- Here laws of thermodynamics include the four laws which in turn include enthalpy, entropy, internal energy and also Gibbs free energy.
- Among the four laws the first law of thermodynamics gives the relationship of energy of the system with that of heat, work and internal energy of the system.
- The first law states that “energy can neither be created nor destroyed but can be converted to another form with the interaction of heat, work and also internal energy”. This is given by,
$\Delta U = Q - W$
where, $\Delta U$ = Change in internal energy
$Q$ = Heat energy and $W$= work done by the system.

- According to thermochemistry, the above equation according to the definition can be written as,
\[\Delta H=\Delta U+\Delta nRT\]
where,\[\Delta H\] is the heat exchanged between system and the surroundings
 $\Delta U$ is the change in internal energy of the system
and $\Delta nRT$ is the work done by the system or on the system.
So, the correct answer is “Option A”.

Note: Note that thermochemistry is only the part of thermodynamics which studies the relationship between heat and chemical reactions and also not to confuse that answer could be option D) thinking that $\Delta U$ is always negative and note that it is the negative quantity but when multiplied to other negative sign it becomes positive.