0700-1-cre-1mark

Collision theory states that the rate constant \(k\) is proportional to

• \(T\)

• \(Te^{-E/RT}\)

• \(e^{-E/RT}\)

• \(T^{1/2}e^{-E/RT}\)

GATE-CH-1988-7-b-ii-cre-1mark

In transition-state theory, the rate of the reaction is derived by assuming that the activated complex is in equilibrium with

• the products

• the reactants

• both reactants and products

• none of the above

GATE-CH-1989-7-i-a-cre-1mark

From the stoichiometry, one can say that the following reaction is non-elementary. \[ \ce {N2} + 3\ce {H2} \Leftrightarrow 2 \ce {NH3} \] The reason is

• No elementary reaction has an order greater than 3

• The order of the forward reaction is not the same as that of the backward reaction

• The reaction takes place in gas phase only

• None of the above

GATE-CH-1989-7-i-c-cre-2mark

The rate constant for a particular reaction becomes 100 times as large when the temperature is increased from 400 K to 500 K. Assuming that the transition state theory is valid, the value of \((E/R)\), i.e., the activation energy divided by the gas constant is:

• 8987 K

• 9210 K

• 8764 K

• 8621 K

GATE-CH-1990-7-iii-cre-2mark

In a homogeneous gas phase reaction \(A + 2B \rightarrow R + S\) what is the relationship between \(r_{A}\) and \(r_{B}\):

• \(2 r_{A} = r_{B}\)

• \(r_{A} = 2 r_{B}\)

• \(r_{A} = r_{B}\)

• None of the above

GATE-CH-1992-8-b-cre-2mark

The units of frequency factor in Arrhenius equation

• are the same as those of the rate constant

• depend on the order of the reaction

• depend on temperature, pressure etc. of the reaction

• are cycles per unit time

GATE-CH-1996-1-3-cre-1mark

From collision theory, the reaction rate constant is proportional to

• \(\displaystyle \exp \left (-\frac {E}{RT}\right )\)

• \(\displaystyle \exp \left (-\frac {E}{2RT}\right )\)

• \(\sqrt {T}\)

• \(\displaystyle T^m\exp \left (-\frac {E}{RT}\right )\)

GATE-CH-1998-1-20-cre-1mark

Molecularity of an elementary reaction \(P +Q \rightarrow R + S\) is

• 1

• 2

• 3

• 4

GATE-CH-1999-1-21-cre-1mark

Overall order of reaction for which the rate constant has units of (mol/litre)\(^{-3/2}\).s\(^{-1}\) is

• \(-3/2\)

• 1/2

• 3/2

• 5/2

GATE-CH-1999-1-22-cre-1mark

For the reaction \(A + B \rightarrow 2B + C\),

• \(r_{A} = r_{B}\)

• \(r_{A} = -r_{B}\)

• \(r_{A} = 2r_{B}\)

• \(r_{A} = r_{B}/2\)

GATE-CH-1999-2-15-cre-2mark

At a given value of \(E/R\) (ratio of activation energy and gas constant), the ratio of the rate constants at 500 K and 400 K is 2 if Arrhenius law is used. What will be this ratio if transition-state theory is used with the same value of \(E/R\)?

• 1.6

• 2

• 2.24

• 2.5

GATE-CH-2000-1-18-cre-1mark

The experimentally determined overall order for the reaction \[ A + B \rightarrow C + D \] is two. Then the

• reaction is elementary with a molecularity of 2

• molecularity of the reaction is 2, but the reaction may not be elementary

• reaction may be elementary with a molecularity of 2

• reaction is elementary but the molecularity may not be 2

GATE-CH-2001-1-15-cre-1mark

The reaction rate constants at two different temperatures \(T_1\) and \(T_2\) are related by

• \(\displaystyle \ln \left (\frac {k_2}{k_1}\right ) = \frac {E}{R}\left (\frac {1}{T_2} - \frac {1}{T_1}\right )\)

• \(\displaystyle \ln \left (\frac {k_2}{k_1}\right ) = \frac {E}{R}\left (\frac {1}{T_1} - \frac {1}{T_2}\right )\)

• \(\displaystyle \exp \left (\frac {k_2}{k_1}\right ) = \frac {E}{R}\left (\frac {1}{T_1} - \frac {1}{T_2}\right )\)

• \(\displaystyle \exp \left (\frac {k_2}{k_1}\right ) = \frac {E}{R}\left (\frac {1}{T_2} - \frac {1}{T_1}\right )\)

GATE-CH-2003-21-cre-1mark

Find a mechanism that is consistent with the rate equation and the reaction given below: \[ 2A + B \rightarrow A_2B \quad \quad \quad -r_A = kC_AC_B \]

• \(A + B \rightleftharpoons AB; \quad \quad AB + A \rightarrow A_2B\)

• \(A + B \rightarrow AB; \quad \quad AB + A \rightarrow A_2B\)

• \(A + A \rightarrow AA; \quad \quad AA + B \rightarrow A_2B\)

• \(A + A \rightleftharpoons AA; \quad \quad AA + B \rightarrow A_2B\)

GATE-CH-2004-10-cre-1mark

The rate expression for the gaseous phase reaction CO + 2H₂ \(\rightleftharpoons \) CH₃OH is given by \[ r = k_1p^\alpha _{\text {CO}} p^\beta _{\text {H$_2$}} - k_2p^\gamma _{\text{CH$_3$OH}} \]  Which of the following is NOT possible?

• \(\alpha = 1, \beta = 1, \gamma = 1\)

• \(\alpha = 1, \beta = 2, \gamma = 1\)

• \(\alpha = 1/3, \beta = 2/3, \gamma = 1/3\)

• \(\alpha = 1/2, \beta = 1, \gamma = 1/2\)

GATE-CH-2004-23-cre-1mark

The rate of ammonia synthesis for the reaction N₂ + 3H₂ \(\rightleftharpoons \) 2NH₃ is given by \[ r = 0.8 p_{\text {N}_2}p_{\text {H}_2}^3-0.6p_{\text {NH}_3}^2 \] If the reaction is represented as, \(\displaystyle \frac {1}{2}\text {N}_2 + \frac {3}{2}\text {H}_2 \rightleftharpoons \text {NH}_3 \), the rate of ammonia synthesis is

• \( r = 0.8p_{\text {N}_2}^{0.5}p_{\text {H}_2}^{1.5} - 0.6p_{\text {NH}_3}\)

• \( r = 0.8p_{\text {N}_2}p_{\text {H}_2}^{3} - 0.6p_{\text {NH}_3}^2\)

• \(r = 0.5\big (0.8p_{\text {N}_2}p_{\text {H}_2}^{3} - 0.6p_{\text {NH}_3}^2\big )\)

• \(r = 0.5\big (0.8p_{\text {N}_2}^{0.5}p_{\text {H}_2}^{1.5} - 0.6p_{\text {NH}_3}\big )\)

GATE-CH-2005-25-cre-1mark

For the reaction \(2R + S \rightarrow T\), the rates of formation, \(r_R\), \(r_S\) and \(r_T\) of the substances \(R\), \(S\) and \(T\) respectively, are related by

• \(2  r_R = r_S = r_T\)

• \(2  r_R = r_S = -r_T\)

• \( r_R = 2  r_S = 2  r_T\)

• \( r_R = 2  r_S = -2 r_T\)

GATE-CH-2005-27-cre-1mark

Which is the correct statement from the following statements on the Arrhenius model of the rate constant \(k = Ae^{-E/RT}\)?

• \(A\) is always dimensionless

• For two reactions 1 and 2, if \(A_1 = A_2\) and \(E_1 > E_2\), then \(k_1(T) > k_2(T)\)

• For a given reaction, the % change of \(k\) with respect to temperature is higher at lower temperatures

• The % change of \(k\) with respect to temperature is higher for higher \(A\)

GATE-CH-2005-67-cre-2mark

The rate expression for the reaction of \(A\) is given by \[ -r_A = \frac {k_1C_A^2}{1+k_2C_A^{1/2}} \] The units of \(k_1\) and \(k_2\) are, respectively,

• (mol^-1.m³.s^-1), (mol\(^{-1/2}\).m\(^{3/2}\))

• (mol^-1.m³.s^-1), (mol\(^{1/2}\).m\(^{-3/2}\))

• (mol.m\(^{-3}\).s^-1), (mol\(^{1/2}\).m\(^{-3/2}\).s^-1)

• (mol^-1.m³.s^-1), (mol\(^{-1/2}\).m\(^{3/2}\).s\(^{-1/2}\))

GATE-CH-2015-17-cre-1mark

Which of the following can change if only the catalyst is changed for a reaction system?

• Enthalpy of reaction

• Activation energy

• Free energy of the reaction

• Equilibrium constant

GATE-CH-2016-14-cre-1mark

For a non-catalytic homogeneous reaction \(A \rightarrow B\), the rate expression at 300 K is \[ -r_A  \quad (\text {mol.m$^{-3}$.s$^{-1}$})=\frac {10C_A}{1+5C_A} \] where \(C_A\) is the concentration of \(A\) (in mol/m³). Theoretically, the upper limit for the magnitude of the reaction rate (\(-r_A\) in mol.m\(^{-3}\).s^-1, rounded off to the first decimal place) at 300 K is ____________

• Answer

GATE-CH-2016-16-cre-1mark

Hydrogen iodide decomposes through the reaction 2HI \(\rightleftharpoons \) H₂ + I₂. The value of the universal gas constant \(R\) is 8.314 J.mol^-1.K^-1. The activation energy for the forward reaction is 184000 J/mol. The ratio (rounded off to the first decimal place) of the forward reaction rate at 600 K to that at 550 K is ____________

• Answer

GATE-CH-1994-3-l-cre-1mark

If the rate of the irreversible reaction \(A + B \rightarrow 2C\) is \(kC_AC_B\), then the reaction is always elementary. (True / False)

• True
• False

GATE-CH-1994-3-o-cre-1mark

The mechanism for the decomposition of \(\ce {CH3CHO}\) into \(\ce {CH4}\) and \(\ce {CO}\) in the presence of \(\ce {I2}\) is \[ \begin {align*} \ce {CH3CHO} + \ce {I2} &\rightarrow \ce {CH3I} + \ce {HI} + \ce {CO}; \text { slow} \\
\ce {CH3I} + \ce {HI} &\rightarrow \ce {CH4} + \ce {I2}; \text { fast} \end {align*} \] Then, the rate of disappearance of \(\ce {CH3CHO}\) is equal to \(kC_{\ce {CH3I}}C_{\ce {HI}}\) and \(\ce {HI}\) acts as a catalyst. (True / False)

• True
• False

GATE-CH-2006-49-cre-2mark

A drug tablet of mass \(M_0\) administered orally at time \(t = 0\), reaches the intestine at time \(t = \tau \) without losing any mass. From the intestine, the drug is absorbed into blood. The rate of absorption is found to be proportional to the mass of the drug in the intestine with the proportionality constant \(k\). Assuming no drug is lost from the blood, the total mass of the drug in the blood, \(M_b\), at time \(t > \tau \) is given by

• \(M_b=M_0\big [1-\exp \{-k(t-\tau )\}\big ]\)

• \(M_b=M_0\big [1-\exp \{-kt\}\big ]\)

• \(M_b=M_0\exp \{-k(t-\tau )\}\)

• \(M_b=M_0\big [1-\exp \{-k(t+\tau )\}\big ]\)

GATE-CH-2006-50-cre-2mark

The rate \(r\) at which an antiviral drug acts increases with its concentration in the blood, \(C\), according to the equation, \(r = \dfrac {kC}{C_{50}+C}\) where \(C_{50}\) is the concentration at which the rate is 50% of the maximum rate \(k\). Often, the concentration \(C_{90}\), when the rate is 90% of the maximum, is measured instead of \(C_{50}\). The rate equation then becomes

• \(r=\dfrac {1.8kC}{(C_{90}+C)}\)

• \(r=\dfrac {kC}{\left (\dfrac {C_{90}}{9}+C\right )}\)

• \(r=\dfrac {kC}{C_{90}}\)

• \(r=\dfrac {0.9kC}{C_{90}}\)

GATE-CH-2013-40-cre-2mark

The gas phase decomposition of azomethane to give ethane and nitrogen takes place according to the following sequence of elementary reactions. 

\[ \begin {align*} (\text {CH}_3)_2\text {N}_2 + (\text {CH}_3)_2\text {N}_2 &\stackrel {k_1}{\longrightarrow } (\text {CH}_3)_2\text {N}_2 + [(\text {CH}_3)_2\text {N}_2]^* \\ [(\text {CH}_3)_2\text {N}_2]^* + (\text {CH}_3)_2\text {N}_2 &\stackrel {k_2}{\longrightarrow } (\text {CH}_3)_2\text {N}_2 + (\text {CH}_3)_2\text {N}_2 \\ [(\text {CH}_3)_2\text {N}_2]^* &\stackrel {k_3}{\longrightarrow } \text {C}_2\text {H}_6 + \text {N}_2 \end {align*} \]

Using the pseudo-steady-state-approximation for \([(\text {CH}_3)_2\text {N}_2]^*\), the order with respect to azo-methane in the rate expression for the formation of ethane, in the limit of high concentrations of azomethane, is ____________

• Answer

GATE-CH-1988-17-i-cre-6mark

The decomposition of \(\ce {N2O5}\) is postulated to occur by the following mechanism: \[ \begin {align*} \ce {N2O5 & <=>[k_1][k_2] NO2 + NO3^*} \\
\ce {NO3^*} &\stackrel {k_3}{\rightarrow } \ce {NO^*} + \ce {O2} \\
\ce {NO^*} + \ce {NO3^*} &\stackrel {k_4}{\rightarrow } 2\ce {NO2} \end {align*} \] Using the steady state approximation, derive an expression for the rate of decomposition of \(\ce {N2O5}\).

• Answer

GATE-CH-1990-17-i-cre-2mark

For a unimolecular gas phase reaction \(A\rightarrow \) Products, the reaction mechanism is given by \(r = \dfrac {k_1k_3[A]^2}{k_2[A]+k_3}\). What would be the order of this reaction at very high and very low pressures?

• Answer

GATE-CH-1992-8-d-cre-2mark

In a first-order reaction \(A\rightarrow \text {Products}\), the reaction rate becomes slower as it proceeds, because the concentration of \(A\) ––––- , and the rate is ––––-

• Answer