One mole of an ideal gas at 900 K, undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $$\ln {{{V_3}} \over {{V_2}}}$$ is _________.
(U : internal energy, S : entropy, p : pressure, V : volume, R : gas constant)
(Given : molar heat capacity at constant volume, CV,m of the gas is $${5 \over 2}$$R)
Your Input ________
Answer
Correct Answer is 10
Explanation
For process 1, entropy is constant thus, q is constant
$$\therefore$$ $${W_I} = \Delta U = n{C_{V,m}}\Delta T$$
For the reaction, X(s) $$\rightleftharpoons$$ Y(s) + Z(g), the plot of $$\ln {{pz} \over {{p^\theta }}}$$ versus $${{{{10}^4}} \over T}$$ is given below (in solid line), where pz is the pressure (in bar) of the gas Z at temperature T and $${{p^\theta }}$$ = 1 bar.
(Given, $${{d(\ln K)} \over {d\left( {{1 \over T}} \right)}} = - {{\Delta {H^\theta }} \over R}$$, where the equilibrium constant, $$K = {{pz} \over {{p^\theta }}}$$ and the gas constant, R = 8.314 J K$$-$$1 mol$$-$$1)
The value of $$\Delta$$S$$\theta$$ (in J K$$-$$1 mol$$-$$1) for the given reaction, at 1000 K is _________.
Your Input ________
Answer
Correct Answer is 141.34
3
JEE Advanced 2021 Paper 1 Online
Numerical
For the reaction, X(s) $$\rightleftharpoons$$ Y(s) + Z(g), the plot of $$\ln {{pz} \over {{p^\theta }}}$$ versus $${{{{10}^4}} \over T}$$ is given below (in solid line), where pz is the pressure (in bar) of the gas Z at temperature T and $${{p^\theta }}$$ = 1 bar.
(Given, $${{d(\ln K)} \over {d\left( {{1 \over T}} \right)}} = - {{\Delta {H^\theta }} \over R}$$, where the equilibrium constant, $$K = {{pz} \over {{p^\theta }}}$$ and the gas constant, R = 8.314 J K$$-$$1 mol$$-$$1)
The value of standard enthalpy, $$\Delta$$H$$\theta$$ (in kJ mol$$-$$1) for the given reaction is _______.
Your Input ________
Answer
Correct Answer is 166.28
4
JEE Advanced 2020 Paper 1 Offline
Numerical
Aluminium reacts with sulphuric acid to form aluminium sulphate and hydrogen. What is the volume of hydrogen gas in litre (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulphuric acid are combined for the reaction?
(Use molar mass of aluminium as 27.0 g mol$$-$$1, R = 0.082 atm L mol$$-$$1 K$$-$$1)
Your Input ________
Answer
Correct Answer is 6.15
Explanation
Aluminium reacts with sulphuric acid to form aluminium sulphate and hydrogen.
