Question

For the reaction,
${{C}_{3}}{{H}_{8}}(g)+5{{O}_{2}}(g)\to 3C{{O}_{2}}(g)+4{{H}_{2}}O(l)$ at constant temperature, $\Delta H-\Delta E$ is …………
A. –RT
B. -3RT
C. +3RT
D. None of these

Answer 1

Hint: The first law of thermodynamics is generally a law of conservation of energy which distinguishes the two kinds of transfer of energy as heat and as thermodynamic work and relates them to a function of a body’s state known as Internal energy.

Complete Step by step solution:
The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed. We know the equation:
$\Delta H=\Delta E+P\Delta V$
Where, $\Delta H$ corresponds to change in enthalpy, $\Delta E$ change in energy, P is pressure and $\Delta V$ change in the volume. This equation can be written as:
$\Delta H-\Delta E=P\Delta V$
There is another equation about what we know is
$P\Delta V=\Delta nRT$
Put the value in above equation:
$\Delta H-\Delta E=\Delta nRT$
Where $\Delta n$ corresponds to change in moles from reactant to product which can be calculated as:
$\Delta n=3-6=-3$
\[\Delta H-\Delta E=-3RT\]

Hence from the above calculations we conclude that option B is the correct answer.

Note: $\Delta G$ quantity is generally temperature-dependent i.e. value can be increased or decreased with increasing or decreasing temperature and if we assume $\Delta H$ and $\Delta S$ are independent of temperature when there is no phase change in the reaction. So if we know the value of $\Delta H$ and $\Delta S$ we can easily find out the value of $\Delta G$ at any temperature.