Question

For the real gases reaction $2C{O_{\left( g \right)}} + {O_{2\left( g \right)}} \to 2C{O_{2\left( g \right)}}$ : $\Delta {\rm H} = - 560$ $kJ$ .In $10$ litre rigid vessel at $500K$ .The initial pressure is $70$ bar and after the reaction it becomes $40$ bar. The change in internal energy is
(A) $- 557$ $kJ$
(B) $- 530$ $kJ$
(C) $- 563$ $kJ$
(D) None of these

Answer 1

Hint : Internal energy is composed of kinetic energy as well as potential energy of the constituents present in the system. It is represented as $\left( U \right)$ .Value of internal energy is either positive or negative depending upon the reaction condition.

Complete Step By Step Answer:
Enthalpy is related to internal energy of the system, pressure of the system and volume of the system. The mathematical expression for such relationship is
${\rm H} = U + pV$
Where $H$ is enthalpy of the system
$U$ Is internal energy of system
$p$ Pressure of system
$V$ Volume of system.
From the given problem we see that reaction is carried out in a vessel of fixed capacity of $10$ litre. Hence the reaction proceeds under the isochoric condition.
Therefore, the equation modified and become-
$\Delta H = \Delta U + \left( {{p_1} - {p_2}} \right)V$
Where ${p_1}$ is initial pressure of system as given $70$ bar
${p_2}$ is final pressure of system as given $40$ bar
$\Delta {\rm H} = - 560$ $kJ$ is enthalpy of system
$V$ is volume of system as given $10$ litre
Now put all the values in the equation
$- 560 = \Delta U + \left( {70 - 40} \right)10$
$- 560 = \Delta U + \left( {30} \right)10$
On simplifying the equation, we get
$- 560 = \Delta U + 300$
Convert the value of $300$ litre-atmosphere into $300kJ$ by multiplying $\left( {0.1} \right)$
$- 560 = \Delta U + 300 \times 0.1$
Rearrange the equation in terms of internal energy of system
$\Delta U = - 560 + 30$
$\Delta U = 530$ $kJ$
Hence, the change in internal energy is $530kJ$ .Therefore, option $\left( 2 \right)$ is the correct option.

Note :
Internal energy is a type of state function which is dependent upon the initial and final states of the chemical reaction.
Reaction process under constant volume condition is known as isochoric process.