Question

For the reaction , \[A(g) + 2B(g) \to 2C(g) + 3D(g)\] , the change in enthalpy at \[{27^O}C\] is\[19kCal\]. The value of \[\Delta E\] is?
A.\[10.5\] \[kCal\]
B.\[28.9\] \[kCal\]
C.\[17.8\] \[kCal\]
D.\[19\] \[kCal\]

Answer 1

Hint: The change of enthalpy is a standard term given to the change in heat i.e. the amount of heat evolved or absorbed during a chemical reaction at a constant pressure. While the internal energy of the system is the energy required by that system to be stable. It is denoted by\[\Delta E\].

Complete answer:
The change of enthalpy is denoted by\[\Delta H\]. It is the amount of heat absorbed or released.
So in order to proceed with this question, let’s start by finding the change in number of moles from reactant to product.
Formula to calculate \[\Delta {n_g}\] is –
Since the reaction is \[A(g) + 2B(g) \to 2C(g) + 3D(g)\]
So, \[\Delta {n_g}\] \[ = {n_P} - {n_R}\]
Hence, \[\Delta {n_g}\]
   = 5 - 3
   = 2
And \[\Delta H = 19kCal = 19 \times {10^3}\]
This change in enthalpy will be utilised
 Temperature, \[273 + 27 = 300\]
R \[ = 2\]
Hence, we know the formula to calculate the change in internal energy as –
\[\Delta E = \Delta H - \Delta {n_g}RT\]
Hence by putting the values
\[ = 19 \times {10^3} - (2 \times 2 \times 300) \]
\[ = 17.8kCal \]
Therefore by putting all the values in the equation and solving the equation, we obtained our answer as \[17.8\] \[kCal\], this is the change in internal energy of the system which is needed thermodynamically to maintain its system.

So , our option C is correct .

Note:
Here R used is actually a gas constant that has its fixed value of 2 in the calorie unit system. It is always fixed. And the temperature was given in the Celsius system, so we will calculate it in the kelvin system, simply by adding the value \[273 + 27 = 300\] . So this is an easy and effective method to calculate any value using this formula.