Thermodynamics Test

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Thermodynamics Test - 80

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Weekly Quiz Competition

Question 1
1 / -0

$$\Delta { G }^{ o }$$ of the cell reaction $$AgCl(s)+\cfrac { 1 }{ 2 } { H }_{ 2 }(g)=Ag(s)+{ H }^{ + }+{ Cl }^{ - }$$ is $$-21.52kJ$$. $$\Delta { G }^{ o }$$ of
$$2AgCl(s)+{ H }_{ 2 }(g)=2Ag(s)+2{ H }^{ + }+2{ Cl }^{ - }$$

A
$$-21.52kJ$$

B
$$-10.76kJ$$

C
$$-43.04kJ$$

D
$$43.04kJ$$

Solution

since $$\Delta G$$ is an extensive property $$\Delta { G }_{ 2 }=2\Delta { G }_{ 1 }\quad $$

$$\Delta g = 2\times -21.52 = 43.04\ KJ$$
Question 2
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In which case is a reaction impossible at any temperature?

A
$$\Delta H > 0, \Delta S > 0$$

B
$$\Delta H > 0, \Delta S < 0$$

C
$$\Delta H < 0, \Delta S < 0$$

D
In all cases

Solution

$$\Delta G=+ve$$ if $$\Delta H =+ve$$ and $$\Delta S=-ve$$. which is non spontaneous condition at any temp.

Hence, option B is correct.
Question 3
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The equilibrium partial pressure of $$N_2, H_2$$ and $$NH_3$$ are $$4, 4$$ and $$8$$ atm respectively. The value of $$K_p$$ for the Haber's process in $$atm^{-1}$$ is:

A
$$1/4$$

B
$$1/2$$

C
$$4$$

D
$$2$$

Solution
Question 4
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For the expression : $$dG = Vdp - SdT,$$ which of the following is correct?

A
$$\left ( \dfrac{\partial G}{\partial T} \right )_{p} = V$$

B
$$\left ( \dfrac{\partial G}{\partial p} \right )_{T} = V$$

C
$$\left ( \dfrac{\partial G}{\partial T} \right )_{S} = V$$

D
$$\left ( \dfrac{\partial G}{\partial p} \right )_{V} = V$$

Solution

A) $$\left ( \dfrac{\partial G}{\partial T} \right )_{p} = S$$

B) $$\left ( \dfrac{\partial G}{\partial p} \right )_{T} = V$$

C) $$\left ( \dfrac{\partial G}{\partial T} \right )_{S} = V\cfrac{\partial p}{\partial T }-S$$

D) $$\left ( \dfrac{\partial G}{\partial p} \right )_{V} = V -S\cfrac{\partial T}{\partial p}$$

Hence, Option "B" is the correct answer.
Question 5
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The Gibbs energy for decomposition of $$Al_2O_3$$ at $$500^oC$$ is as follows:
$$\dfrac {2}{3}Al_2O_3\to \dfrac {4}{3}Al+O_2$$; $$\quad \Delta G=+966\ kJ$$
The potential difference needed for electrolysis reduction of $$Al_2O_3$$ at $$500^oC$$ is at least

A
$$4.5\ V$$

B
$$3.0\ V$$

C
$$2.5\ V$$

D
$$5.0\ V$$

Solution

The ionic reaction taking place in decomposition of $$\mathrm{Al_2O_3}$$ are:

$$\mathrm{\cfrac{2}{3}(2Al^{+3}) +4e^- \longrightarrow \cfrac{4}{3}Al}$$ & $$\mathrm{\cfrac{2}{3}(3O^{-2}) \longrightarrow O_2 + 4e^-}$$

So, the no. of electrons involved = 4 i.e. n=4.

$$\mathrm{\because \ \Delta G= -nFE}$$

$$\mathrm{\implies \ 966 \times 10^3= -4\times 96600\times E}$$

$$\mathrm{\implies E=-2.5 \ V}$$

Hence, Option "C" is the correct answer.
Question 6
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Directions For Questions

The contributions of both heat (enthalpy) and randomness (entropy) shall be considered to the overall spontaneity of a process .When deciding about the spontaneity of a chemical reaction or other process, we define a quantity called the Gibb's energy change $$(\Delta G)$$
$$\Delta G = \Delta H-T\Delta S$$
where, $$\Delta H$$=Enthalpy change; $$\Delta S$$=Entropy change; T=Temperature in kelvin.
If $$\Delta G < 0$$,Process is spontaneous; $$\Delta G=0$$, Process is at equilibrium, $$\Delta G > 0$$ , Process is non-spontaneous.

...view full instructions

For the change $$H_2O(s), (273 K, 2 atm) \rightarrow H_2O(l), (273 K, 2 atm)$$, choose the correct option.

A
$$\Delta G =0$$

B
$$\Delta G < 0$$

C
$$\Delta G > 0$$

D
None

Solution

$$H_2O (s) \rightarrow H_2O (l)$$

At P=1 atm, $$\Delta G =0$$, there is equilibrium at 273 K.

since reaction in forward direction so $$\Delta$$G is less than 0 spontanesous process.
Question 7
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$$10 l t$$ box contains $$O_3$$ and $$O_2$$ at equilibrium at $$2000 K$$. The $$\triangle G^o = -534.52 kJ$$ at $$8$$ atm equilibrium pressure. The following equilibrium is present in the container
$$2O_3(g) \rightleftharpoons 3O_2(g)$$. The partial pressure of $$O_3$$ will be (ln $$10 = 2.3, R = 8.3 J \;\ mole^{-1} K^{-1}$$.

A
$$8 \times 10^{-6}$$

B
$$22.62 \times 10^{-7}$$

C
$$9.71 \times 10^{-6}$$

D
$$9.71 \times 10^{-2}$$

Solution

$$\triangle G^o = -RT$$ In $$K=-2.3 \times 2000 \times 8.3 \log K$$

$$\dfrac{534.52 \times 10^3}{2.3 \times 8.3 \times 2000} = \log K$$

$$K= 10^{14}$$

$$2O_3(g) \rightleftharpoons 3O_2(g)$$ $$K=10^{14}$$

So $$Po_3 <<< Po_2$$

So $$Po_2 + Po_3 = 8$$

$$Po_2 = 8$$ atm

$$K = 10^{14} = \dfrac{(Po_2)^3}{(Po_3)^2} = \dfrac{(8)^3}{(Po_3)^2}$$

$$Po_3 = 22.62 \times 10^{-7}$$ atm.
Question 8
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Hess law is based on:

A
Law of conservation of mass

B
Law of conservation of energy

C
Enthalpy is a state function

D
None of these

Solution

The enthalpy change for the overall process is the sum of the enthalpy change of the steps in the process.
This law is conservation of energy
Question 9
1 / -0

In a thermodynamic system working subtance is ideal gas, its internal energy is in the from of

A
Kinetic energy only

B
Kinetic and potential energy

C
Potential energy

D
None of these

Solution

Internal energy is associated with the atoms or molecules of the gas.
In an ideal gas the energy is in the form of Kinetic energy only.
Question 10
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For the reaction, $$A_{\left ( s \right )}+3B_{\left ( g \right )}\rightarrow 4C_{\left ( s \right )}+D_{\left ( l \right )}$$.
$$\Delta H$$ and $$\Delta U$$ are related as:

A
$$\Delta H=\Delta U$$

B
$$\Delta H=\Delta U+3RT$$

C
$$\Delta H=\Delta U+RT$$

D
$$\Delta H=\Delta U-3RT$$

Solution

(D) $$A_{\left ( s \right )}+3B_{\left ( g \right )}\rightarrow 4C_{\left ( s \right )}+D_{\left ( l \right )}$$

$$\Delta n_{g}=0-3=-3;$$

$$\Delta H=\Delta E+\Delta n_{g}RT$$ {$$\because \Delta E=\Delta U$$}

therefore, $$\Delta H=\Delta U-3RT$$

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Thermodynamics Test - 80

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Thermodynamics Test - 80

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Question 1

$$-21.52kJ$$

$$-10.76kJ$$

$$-43.04kJ$$

$$43.04kJ$$

Solution

Question 2

$$\Delta H > 0, \Delta S > 0$$

$$\Delta H > 0, \Delta S < 0$$

$$\Delta H < 0, \Delta S < 0$$

In all cases

Solution

Question 3

$$1/4$$

$$1/2$$

$$4$$

$$2$$

Solution

Question 4

$$\left ( \dfrac{\partial G}{\partial T} \right )_{p} = V$$

$$\left ( \dfrac{\partial G}{\partial p} \right )_{T} = V$$

$$\left ( \dfrac{\partial G}{\partial T} \right )_{S} = V$$

$$\left ( \dfrac{\partial G}{\partial p} \right )_{V} = V$$

Solution

Question 5

$$4.5\ V$$

$$3.0\ V$$

$$2.5\ V$$

$$5.0\ V$$

Solution

Question 6

$$\Delta G =0$$

$$\Delta G < 0$$

$$\Delta G > 0$$

None

Solution

Question 7

$$8 \times 10^{-6}$$

$$22.62 \times 10^{-7}$$

$$9.71 \times 10^{-6}$$

$$9.71 \times 10^{-2}$$

Solution

Question 8

Law of conservation of mass

Law of conservation of energy

Enthalpy is a state function

None of these

Solution

Question 9

Kinetic energy only

Kinetic and potential energy

Potential energy

None of these

Solution

Question 10

$$\Delta H=\Delta U$$

$$\Delta H=\Delta U+3RT$$

$$\Delta H=\Delta U+RT$$

$$\Delta H=\Delta U-3RT$$

Solution

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