﻿ Reaction Equilibrium - Thermodynamics - GATE Questions - with Solutions at MSubbu Academy

## Reaction Equilibrium

### GATE-CH-1988-6-b-ii-td-1mark

1988-6-b-ii-td

Criterion of a chemical equilibrium is that the total Gibbs free energy change is:

• always positive

• always negative

• zero

• not specifically defined

### GATE-CH-1997-1-21-td-1mark

1997-1-21-td

The equilibrium constant $$K$$ for a chemical reaction depends on

• temperature only

• pressure only

• temperature and pressure

• ratio of reactants

### GATE-CH-1997-1-22-td-1mark

1997-1-22-td

The decomposition of $$A$$ into $$B$$ is represented by the exothermic reaction $$A \rightleftharpoons B$$. To achieve maximum decomposition, it is desirable to carry out the reaction

• at high $$P$$ and high $$T$$

• at low $$P$$ and high $$T$$

• at low $$P$$ and low $$T$$

• at high $$P$$ and low $$T$$

### GATE-CH-2002-1-9-td-1mark

2002-1-9-td

The extent of reaction is

• different for reactants and products

• dimensionless

• dependent on the stoichiometric coefficients

• all of the above

### GATE-CH-2004-7-td-1mark

2004-7-td

For an ideal gas mixture undergoing a reversible gaseous phase chemical reaction, the equilibrium constant

• is independent of pressure

• increases with pressure

• decreases with pressure

• increases/decreases with pressure depending on the stoichiometric coefficients of the reaction

[Index]

### GATE-CH-2006-32-td-2mark

2006-32-td

For a reversible exothermic gas phase reaction, $$A+B\rightleftharpoons C$$, the equilibrium conversion will increase with

• increase in pressure and increase in temperature

• decrease in pressure and increase in temperature

• increase in pressure and decrease in temperature

• decrease in pressure and decrease in temperature

### GATE-CH-2012-9-td-1mark

2012-9-td

For an exothermic reversible reaction, which one of the following correctly describes the dependence of the equilibrium constant ($$K$$) with temperature ($$T$$) and pressure ($$P$$)?

• $$K$$ is independent of $$T$$ and $$P$$

• $$K$$ increases with an increase in $$T$$ and $$P$$

• $$K$$ increases with $$T$$ and decreases with $$P$$

• $$K$$ decreases with an increase in $$T$$ and is independent of $$P$$

### GATE-CH-2014-7-td-1mark

2014-7-td

Match the following:

Group 1 Group 2
P. $$\displaystyle \left (\frac {\partial G}{\partial n_i} \right )_{T,P,n_{j\ne i}}$$ I Arrhenius equation
Q. $$\displaystyle \left (\frac {\partial G}{\partial n_i} \right )_{S,V,n_{j\ne i}}$$ II. Reaction equilibrium constant
R. $$\displaystyle \exp \left (\frac {-\Delta G^\circ _{\text {reaction}}}{RT} \right )$$      III. Chemical potential
S. $$\displaystyle \sum (n_i d\mu _i)_{T,P = 0}$$ IV. Gibbs-Duhem equation

• Q-III, R-I, S-II

• Q-III, R-II, S-IV

• P-III, R-II, S-IV

• P-III, R-IV, S-I

### GATE-MT-2007-66-td-2mark

MT-2007-66-td

Enthalpy of formation at 298 K, $$\Delta H_f^\circ$$ of CO2 and PbO are -393 kJ/mol and -220 kJ/mol, respectively. The enthalpy change for the reaction 2PbO + C $$\rightarrow$$ 2Pb + CO2 is

• -173 kJ

• 15 kJ

• 47 kJ

• 440 kJ

### GATE-CH-2013-5-td-1mark

2013-5-td

A gaseous system contains H2,  I2, and HI, which participate in the gas-phase reaction: $$2\text{HI} \rightleftharpoons \text{H_2} + \text{I_2}$$. At a state of reaction equilibrium, the number of thermodynamic degrees of freedom is ____________

[Index]

### GATE-CH-1997-25-td-5mark

1997-25-td

Ethanol is manufactured by the vapor phase hydration of ethylene according to the reaction: $\ce {C2H4(g)} + \ce {H2O(g)} \rightleftharpoons \ce {C2H5OH(g)}$ The reactor operates at 400 K and 2 bar and the feed is a gas mixture of ethylene and steam in the mole ratio 1:3. The equilibrium constant is 0.25. Estimate the composition (mol%) of the equilibrium mixture.
Assume ideal gas behaviour and take $$f_i^\circ$$ = 1 bar, where $$f_i^\circ$$ is the standard state fugacity of component $$i$$.
(i) % of $$\ce {C2H5OH}$$
{#1}

(ii) % of $$\ce {C2H4}$$
{#2}

### GATE-CH-1998-23-td-5mark

1998-23-td

The reaction $$\ce {N2} + \ce {O2} \rightleftharpoons 2\ce {NO}$$ takes place in the gas phase at 2700$$^\circ$$C and 2025 kPa. The reaction mixture initially comprises 15 mole% oxygen, 77 mole% nitrogen and the rest inerts. The standard Gibb’s free energy change for the reaction is 113.83 kJ/mol at this temperature. Assuming ideal gas behaviour, calculate the composition (in %) of all species at equilibrium.
(i) $$\ce {N2}$$
{#1}

(ii) $$\ce {O2}$$
{#2}

(iii) $$\ce {NO}$$
{#3}

(iv) inerts
{#4}

### GATE-CH-1996-2-10-td-2mark

1996-2-10-td

Given $3\ce {H2} + \ce {CO} = \ce {CH4} + \ce {H2O} \quad K_p = 10^{1.84}$ and $4\ce {H2} + \ce {CO2} = \ce {CH4} + 2\ce {H2O} \quad K_p = 10^{1.17}$ the $$K_p$$ for the reaction $\ce {CO} + \ce {H2O} = \ce {CO2} + \ce {H2}$ is

• $$10^{3.01}$$

• $$10^{-0.67}$$

• $$10^{-3.01}$$

• $$10^{0.67}$$

### GATE-CH-2000-2-06-td-2mark

2000-2-06-td

At a given temperature, $$K_1, K_2$$ and $$K_3$$ are the equilibrium constants for the following reaction 1, 2, 3 respectively:

\begin{align*} \text{CH_4(g)} + \text{H_2O(g)} &\rightleftharpoons \text{CO(g)} + 3 \text{H_2(g)} & (1) \\ \text{CO(g)} + \text{H_2O(g)} &\rightleftharpoons \text{CO_2(g)} + \text{H_2(g)} & (2) \\ \text{CH_4(g)} + 2\text{H_2O(g)} &\rightleftharpoons \text{CO_2(g)} + 4 \text{H_2(g)} & (3) \end{align*}

Then $$K_1, K_2$$ and $$K_3$$ are related as

• $$K_3=K_1K_2$$

• $$K_3=(K_1K_2)^{0.5}$$

• $$K_3=\dfrac {K_1+K_2}{2}$$

• $$K_3=(K_1K_2)^2$$

### GATE-CH-2007-34-td-2mark

2007-34-td

Vapor phase hydration of C2H4 to ethanol by the following reaction $\text {C}_2\text {H}_4\text {(g)} + \text {H}_2\text {O}\text {(g)} \rightleftharpoons \text {C}_2\text {H}_5\text {OH} \text {(g)}$ attains equilibrium at 400 K and 3 bar. The standard Gibbs free energy change of reaction at these conditions is $$\Delta G^\circ =4000$$ J/mol. For 2 moles of an equimolar feed of ethylene and steam, the equation in terms of the extent of reaction $$\varepsilon$$ (in mols) at equilibrium is

• $$\displaystyle \frac {\varepsilon (2-\varepsilon )}{(1-\varepsilon )^2} - 0.3 = 0$$

• $$\displaystyle \frac {(1-\varepsilon )^2}{\varepsilon (2-\varepsilon )} - 0.9 = 0$$

• $$\displaystyle \frac {\varepsilon }{(1-\varepsilon )^2} - 0.3 = 0$$

• $$\displaystyle \frac {\varepsilon (2-\varepsilon )}{(1-\varepsilon )^2} - 0.9 = 0$$

[Index]

### GATE-CH-2008-36-td-2mark

2008-36-td

The standard Gibbs free energy change and enthalpy change at 25oC for the liquid phase reaction $\text {CH}_3\text {COOH}\text {(l)} + \text {C}_2\text {H}_5\text {OH}\text {(l)} \rightarrow \text {CH}_3\text {COOC}_2\text {H}_5\text {(l)} + \text {H}_2\text {O}\text {(l)}$ are given as $$\Delta G^\circ _{298} = -4650$$ J/mol and $$\Delta H^\circ _{298} = -3640$$ J/mol. If the solution is ideal and enthalpy change is assumed to be constant, the equilibrium constant at 95oC is

• 0.65

• 4.94

• 6.54

• 8.65

### GATE-MT-2011-32-td-2mark

MT-2011-32-td

Given:

\begin {align*} 2\text {Cu}\text {(s)} + 0.5\text {O}_2\text {(g)} &= \text {Cu}_2\text {O}\text {(s)} \quad \quad \Delta G^\circ = -162200+69.24T, \quad J \\ 2\text {Cu}\text {(l)} + 0.5\text {O}_2\text {(g)} &= \text {Cu}_2\text {O}\text {(s)} \quad \quad \Delta G^\circ = -188300+88.48T, \quad J \end {align*}

The molar free energy change at 1300 K for the transformation of solid Cu to liquid Cu will be

• 1050 J

• 960 J

• 544 J

• 445 J

### GATE-MT-2012-35-td-2mark

MT-2012-35-td

The reduction of FeO with CO gas in co-current flow is given by the following equation: $\text {FeO} + \text {CO} = \text {Fe} + \text {CO}_2 \quad \quad \Delta G^\circ = 8120 \text { J at 1173 K}$ The ratio of $$\bar {P}_{\text {CO}}/\bar {P}_{\text {CO}_2}$$ for this reaction at 1173 K is

• 0.0

• 0.25

• 0.44

• 2.3

### GATE-CH-1991-17-i-td-6mark

1991-17-i-td

Calculate the fraction of pure ethane that would dehydrogenate at 750 K and 5 atm, if the following reaction goes to equilibrium $\ce {C2H6(g)} \rightleftharpoons \ce {C2H4(g)} + \ce {H2(g)}$ $$\Delta G^{\circ }$$ for the reaction at 750 K = 42.576 kJ. Assume ideal gas behaviour.

### GATE-CH-1994-10-td-5mark

1994-10-td

Ethanol can be prepared by the following vapor phase reaction from ethylene: $\ce {C2H4(g)} + \ce {H2O(g)} \rightleftharpoons \ce {C2H5OH(g)}$ The value of $$\Delta G^\circ$$ for the above reaction at 1 atm and 125$$^\circ$$C is 5040 J. Calculate the conversion obtained if an isothermal reactor operating at 125$$^\circ$$C and 2 atm is fed with a mixture containing 50 mol% ethylene and 50 mol% steam. Assume that equilibrium is reached at the exit of the reactor and gases behave ideally.

### GATE-CH-0200-9-td-5mark

0200-9-td

Compute the equilibrium mole fraction of each of the species in the gas phase reaction $$\ce{CO2}$$ + $$\ce{H2}$$ = $$\ce{CO}$$ + $$\ce{H2O}$$ at 1000 K and at (a) 1 atm total pressure, and (b) at 500 atm total pressure. The reaction equilibrium constant $$K$$ = 0.693 at 1000 K. Standard state is pure gases at 1000 K and 1 atm pressure. Initially there are equal amounts of $$\ce{CO2}$$ and $$\ce{H2}$$ present. The fugacity coefficients at 500 atm pressure for the species are:

 For $$\ce{CO2}$$ 0.99 $$\ce{H2}$$ 1.15 $$\ce{CO}$$ 1.08 $$\ce{H2O}$$ 0.86.

### GATE-CH-1988-6-a-v-td-1mark

1988-6-a-v-td

Activity of a component in solution is defined as the ratio of its --------------- to its ---------------

[Index]