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Match the following Column–I A. Isothermal process B. Adiabatic process C. Isobaric process D. Isochoric process Column–II P. $ q = \triangle U $ Q. $ w = – P \triangle V $ R. $ w = \triangle U $ S. $ w = –n RT ln (V_2/V_1) $

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Explanation

Let's match the processes:

A. Isothermal process (constant temperature) - Work done $ w = –n RT ln (V_2/V_1) $ [S]

B. Adiabatic process (no heat exchange) - Work done $ w = \triangle U $ [R]

C. Isobaric process (constant pressure) - Work done $ w = – P \triangle V $ [Q]

D. Isochoric process (constant volume) - Heat added equals change in internal energy $ q = \triangle U $ [P]

Reasoning question choose the correct statement. Statement–1 : The enthalpy of formation of $H_2O(l)$ is greater than of $H_2O (g) $ . Statement–2: Enthalpy change is negative for the condensation reaction $H_2O (g) \rightarrow H_2O(l) $

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Reasoning question choose the correct statement. Statement–1 : Heat of neutralisation of perchloric acid, $HClO_3$, with NaOH is same as that of HCl with NaOH. Statement–2: Both HCl and $HClO_4$ are strong acids.

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Explanation

Statement –1 is true because the heat of neutralization of perchloric acid, $HClO_4$, with NaOH is the same as that of HCl with NaOH. This is because both $HCl$ and $HClO_4$ are strong acids and completely dissociate in water. Statement –2 is also true because both $HCl$ and $HClO_4$ are strong acids. Therefore, Statement –2 correctly explains Statement –1.

Reasoning question choose the correct statement. Statement–1 : When a gas at high pressure expands against vacuum, the work done is maximum. Statement–2: Work done in expansion depends upon the pressure inside the gas and increase in volume.

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Reasoning question choose the correct statement. Statement I : The chemical reaction, $3H_2(g) + N_2(g) \rightarrow 2NH_3 $ shows decrease in entropy. Statement II: The process passes into equilibrium state when $ \triangle GT,P $ becomes zero.

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Calculate the work performed when 2 moles of hydrogen expand isothermally and reversibly at $25 ^\circ C $ form 15 to 50 litres.

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Explanation

W = – 2.303 n RT log $ { V_2 \over V_1 } = - 2.303 \times 2 \times 2 \times 298 \times log { 50 \over 15 } = -1436 calories $

The $ \triangle H_f0 for CO_2(g), CO(g) and H_2O (g)$ are –393.5, –110.5 and –241.8 $kJ mol^{–1} $ respectively. The standard enthalpy change (in kJ) for the reaction $CO_2(g) + H_2(g) \rightarrow CO(g) + H_2O (g) $ is –

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For reaction carried out in automobiles, what is the value of $ \triangle H , \triangle S and \triangle G ? $ $ 2C_8H_{18} (g) + 25O_2(g) 16CO_2(g)+ 18H_2O(g) $

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At $25 ^\circ $ temperature equilibrium constant Kp for given reaction is $ = 1.8 10 ^{–7} $ Then what is the value of $ \triangle G ^\circ ? PCl_5 \rightleftharpoons PCl_3 + Cl_2 $

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Explanation

$ \triangle G ^\circ = – RT ln Kp $ = – 2.303RT log Kp $ = – 2.303 298 log 1.8 10^ {–7} $ = – 2.303 1.987 298 (– 6.7447) = 9197.5 Cal

The value of $ \triangle H_f ^\circ of U_3O_8 is –853.5 KJ mol^{–1} $ . Also $ \triangle H ^\circ $ for the reaction $3UO_2 + O_2 \rightarrow U_3O_8, $ is –76.00 KJ. The value of $ \triangle H_f ^\circ of UO_2 $ is approx –

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Explanation

To find the enthalpy of formation ($ riangle H_f^ ext{°}$) of $UO_2$, we can use the given data and the enthalpy change of the reaction. The given enthalpy changes are:

$ riangle H_f^ ext{°}(U_3O_8) = -853.5$ kJ/mol and $ riangle H^ ext{°}$ for the reaction $3 UO_2 + O_2 ightarrow U_3O_8$ is $-76.00$ kJ.

Using Hess's law, we can write the enthalpy change for the reaction as:

$ riangle H^ ext{°} = riangle H_f^ ext{°}(U_3O_8) - 3 riangle H_f^ ext{°}(UO_2) - riangle H_f^ ext{°}(O_2)$

Since the enthalpy of formation of $O_2$ in its standard state is zero, we have:

$-76.00 = -853.5 - 3 riangle H_f^ ext{°}(UO_2)$

Rearranging to solve for $ riangle H_f^ ext{°}(UO_2)$:

$3 riangle H_f^ ext{°}(UO_2) = -853.5 + 76.00$

$3 riangle H_f^ ext{°}(UO_2) = -777.5$

$ riangle H_f^ ext{°}(UO_2) = -777.5 / 3 = -259.17$ kJ/mol

Thus, the value of $ riangle H_f^ ext{°}$ of $UO_2$ is approximately $-259.17$ kJ/mol.

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