Question

For $CaC{{O}_{3}}(s)\to CaO(s)+C{{O}_{2}}(g)$at $977{}^\circ C$, $\Delta H=174kJ/mol$; then $\Delta E$is:
A.160 kJ
B. 163.6 kJ
C. 186.4 kJ
D. 180 kJ

Answer 1

Hint: relation between enthalpy change and internal energy can be written in the number of moles as, $\Delta H=\Delta E+\Delta nRT$, where n are the number of moles. This number of moles is moles of reactants subtracted from moles of products. Number of moles is taken only for gaseous species.

Complete answer:
Enthalpy of any reaction is the heat contained in that system at constant pressure. Enthalpy is the sum of internal energy and pressure, volume. As, H = E + PV, where, H is enthalpy, E is internal energy, P is pressure, and V is volume.
This equation can be written in terms of number of moles. This is done by replacing PV with nRT, from the relation of ideal gas equation, as PV = nRT. So, the equation can be,
H = E + nRT, for a reaction taking place, at constant pressure and temperature, there is change in these values, so the equation is,
$\Delta H=\Delta E+\Delta nRT$, we have been given the value of $\Delta H=174kJ/mol$ and temperature of $977{}^\circ C$.
To find number of moles, subtract number of moles of reactants from number of moles of product from the reaction, $CaC{{O}_{3}}(s)\to CaO(s)+C{{O}_{2}}(g)$
As we can see, only 1 product is gaseous, while others are solids, so $\Delta n$ = 1 – 0 = 1, putting all the given values in the formula, $\Delta H=\Delta E+\Delta nRT$, rearranging for internal energy, we have,
$\Delta E=\Delta H-\Delta nRT$
$\Delta E=(-174\times {{10}^{3}})-1(8.314)\times 1250\,J$(converting kJ into J, and Celsius into Kelvin)
$\Delta E=163.6\,kJ$
Hence, for the given reaction, $\Delta E$ is 163.6 kJ.

So, option B is correct.

Note:
The conversion of Celsius to Kelvin is $1{}^\circ C=273K$ , so 273 is added in the Celsius value. The conversion for 1 kilojoule to joule is 1 kJ = 1000 J. So, the value of kJ for enthalpy is converted to Joules. The final answer is expressed in kilojoules by dividing the value obtained in joules by 1000.