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

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

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

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

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

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

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

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

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

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

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

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 ____________

• Answer

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

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

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

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

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

\( \begin{align*} \text{CH$_4$(g)} + \text{H$_2$O(g)} &\rightleftharpoons \text{CO(g)} + 3 \text{H$_2$(g)} & (1) \\ \text{CO(g)} + \text{H$_2$O(g)} &\rightleftharpoons \text{CO$_2$(g)} + \text{H$_2$(g)} & (2) \\ \text{CH$_4$(g)} + 2\text{H$_2$O(g)} &\rightleftharpoons \text{CO$_2$(g)} + 4 \text{H$_2$(g)} & (3) \end{align*} \)

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

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

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

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

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

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

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

The standard Gibbs free energy change and enthalpy change at 25^oC 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 95^oC is

• 0.65

• 4.94

• 6.54

• 8.65

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

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

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

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.

• Answer

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

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.

• Answer

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

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.

• Answer

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

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

• Answer