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.