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55
MCQ (Single Correct Answer)

Assertion (A) Combustion of all organic compounds is an exothermic reaction.

Reason (R) The enthalpies of all elements in their standard state are zero.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
C
$A$ is true but $R$ is false
D
$A$ is false but $R$ is true
56
MCQ (Single Correct Answer)

Assertion (A) Spontaneous process is an irreversible process and may be reversed by some external agency.

Reason (R) Decrease in enthalpy is a contributory factor for spontaneity.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
C
$A$ is true but $R$ is false
D
$A$ is false but $R$ is true
57
MCQ (Single Correct Answer)

Assertion (A) A liquid crystallises into a solid and is accompanied by decrease in entropy. Reason (R) In crystals, molecules organise in an ordered manner.

A
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
B
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$
C
$A$ is true but $R$ is false
D
$A$ is false but $R$ is true
58
Subjective

Derive the relationship between $\Delta H$ and $\Delta U$ for an ideal gas. Explain each term involved in the equation.

Explanation

From the first law of thermodynamics, $\quad q=\Delta U+p \Delta V$

If the process carried out at constant volume, $\Delta V=0$

Hence, $$q_v=\Delta U$$

[Here, $q_v=$ Heat absorbed at constant volume, $\Delta U=$ change in internal energy]

Similarly, $q_p=\Delta H$

Here, $\quad q_p=$ heat absorbed at constant pressure

$\Delta H=$ enthalpy change of the system.

Enthalpy change of a system is equal to the heat absorbed or evolved by the system at constant pressure.

As we know that at constant pressure, $\Delta H=\Delta U+p \Delta V$ where, $\Delta V$ is the change in volume.

This equation can be rewritten as $\Delta H=\Delta U+p\left(V_f-V_i\right)=\Delta U+\left(p V_f-p V_i\right)\quad \text{... (i)}$

where, $$V_i$$ = initial volume of the system $$V_f$$ = final volume of the system

But for the ideal gases, $$p V=n R T$$

So that $$p V_1=n_1 R T$$

and $$p V_2=n_2 R T$$

where, $n_1=$ number of moles of the gaseous reactants

$n_2=$ number of moles of the gaseous products.

Substituting these values in Eq. (i), we get

$$\begin{aligned} & \Delta H=\Delta U+\left(n_2 R T-n_1 R T\right) \\ \text{or}\quad & \Delta H=\Delta U+\left(n_2-n_1\right) R T \end{aligned}$$

where, $\Delta n_g=n_2-n_1$ is the difference between the number of moles of the gaseous products and gaseous reactants.

Putting the values of $\Delta H$ and $\Delta U$ we get

$$q_p=q_v+\Delta n_g R T$$

59
Subjective

Extensive properties depend on the quantity of matter but intensive properties do not. Explain whether the following properties are extensive or intensive.

Mass, internal energy, pressure, heat capacity, molar heat capacity, density, mole fraction, specific heat, temperature and molarity.

Explanation

Extensive properties Those properties whose value depends on the quantity or size of matter present in the system is known as extensive properties.

e.g., mass, internal energy, heat capacity.

Intensive properties Those properties which do not depend on the quantity or size of matter present are known as intensive properties. e.g., pressure, molar heat capacity, density, mole fraction, specific heat, temperature and molarity.

Mole fraction or molarity of a solution is same whether we take a small amount of the solution or large amount of the solution. Ratio of two extensive properties is always intensive.

$\frac{\text { Extensive }}{\text { Extensive }}=$ Intensive

So, mole fraction and molarity are intensive properties.

e.g., $\quad$ mole fraction $=\frac{\text { Moles of the component }}{\text { Total no. of moles }}=\frac{\text { Extensive }}{\text { Extensive }}$

and $\quad$ molarity $=\frac{\text { Mole }}{\text { Volume }}=\frac{\text { Extensive }}{\text { Extensive }}$