Kinetics of Homogeneous Reactions

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

1. \(A\) is always dimensionless

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

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

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

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

1. 1
2. 2
3. 3
4. 4

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

1. \(-3/2\)
2. 1/2
3. 3/2
4. 5/2

1. What is the order (\(n\)) of reaction? (Choose from: 0, 0.5, 1, 2)
2. What is the value of \(k\) in mol, liter, min units? _________ \(\times 10^{-3} \text{ (mol/liter)$^{1-n}$.min$^{-1}$}\) where \(n\) is the order of reaction.

1. first order reaction _______ min
2. second order reaction _______ min

1. What is the order (\(n\)) of reaction? (Choose from: 0, 0.5, 1, 2)
2. What is the value of \(k\) in mol, liter, min units. _______ \(\text{ (mol/liter)$^{1-n}$.min$^{-1}$}\) where \(n\) is the order of reaction.

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 ____________

1. \(k_1 = \)__________ min^-1
2. \(k_2 = \)__________ min^-1

1. \(\dfrac {1}{k_1}\)
2. \(\dfrac {1}{k_2}\)
3. \(\dfrac {1}{k_1-k_2}\)
4. \(\dfrac {1}{k_1+k_2}\)

The rate of the liquid phase reversible reaction \(A \rightleftharpoons 2B\) in (kmol.m^-3.min^-1) at 298 K, is \[ -r_A = 0.02 C_A - 0.01 C_B \] where the concentrations \(C_A\) and \(C_B\) are expressed in (kmol.m^-3). What is the maximum limiting conversion of \(A\) achievable in an isothermal CSTR at 298 K, assuming pure \(A\) is fed at the inlet?

1. 1
2. 2/3
3. 1/2
4. 1/3

1. \(2  r_R = r_S = r_T\)
2. \(2  r_R = r_S = -r_T\)
3. \( r_R = 2  r_S = 2  r_T\)
4. \( r_R = 2  r_S = -2 r_T\)

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

1. \(r_{A} = r_{B}\)
2. \(r_{A} = -r_{B}\)
3. \(r_{A} = 2r_{B}\)
4. \(r_{A} = r_{B}/2\)

Consider the n\(^{\text{th}}\) order irreversible liquid phase reaction \(A \rightarrow B\). Which one of the following plots involving half-life of the reaction \((t_{1/2})\) and the initial reactant concentration \((C_{A0})\) gives a straight line plot?

1. \(C_{A0}\) vs. \(t_{1/2}\)

2. \(\ln C_{A0}\) vs. \(t_{1/2}\)

3. \(C_{A0}\) vs. \(\ln t_{1/2}\)

4. \(\ln C_{A0}\) vs. \(\ln t_{1/2}\)

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 ____________

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

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

2. \(A + B \rightarrow AB; \quad \quad AB + A \rightarrow A_2B\)

3. \(A + A \rightarrow AA; \quad \quad AA + B \rightarrow A_2B\)

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