401. Match each collision-theory quantity in Column I with its description in Column II.
| Column I | Column II |
|---|
| P. Collision frequency, \(Z\) | 1. Fraction accounting for favourable orientation |
| Q. \(e^{-E_a/(RT)}\) | 2. Total encounter frequency |
| R. Steric factor, \(P\) | 3. Energetic fraction of collisions |
| S. Effective-collision frequency | 4. Product of collision, energy, and orientation factors |
ⓐ. P-1, Q-3, R-2, S-4
ⓑ. P-2, Q-3, R-1, S-4
ⓒ. P-2, Q-1, R-4, S-3
ⓓ. P-4, Q-2, R-1, S-3
Correct Answer: P-2, Q-3, R-1, S-4
Explanation: The symbol \(Z\) represents the total frequency of molecular encounters. The exponential term represents the fraction with enough energy to overcome the barrier. The steric factor \(P\) accounts for the fraction with suitable relative orientation. Multiplying these contributions gives the effective-collision frequency. Each factor removes a different class of unsuccessful encounters.
402. The collision-theory expression for a rate constant is commonly written as:
ⓐ. \(k=\frac{PZRT}{E_a}\)
ⓑ. \(k=PZ+e^{-E_a/(RT)}\)
ⓒ. \(k=\frac{e^{E_a/(RT)}}{PZ}\)
ⓓ. \(k=PZe^{-E_a/(RT)}\)
Correct Answer: \(k=PZe^{-E_a/(RT)}\)
Explanation: The total encounter frequency is represented by \(Z\). The exponential factor selects the energetically qualified fraction. The steric factor \(P\) accounts for favourable molecular orientation. Their product gives the simplified collision-theory form \(k=PZe^{-E_a/(RT)}\). This expression resembles the Arrhenius equation, with \(PZ\) corresponding broadly to the pre-exponential contribution.
403. Complete the collision-theory relation.
\[
k=\underline{\hspace{1.2cm}}\,Z e^{-E_a/(RT)}
\]
ⓐ. \(R\)
ⓑ. \(T\)
ⓒ. \(P\)
ⓓ. \(E_a\)
Correct Answer: \(P\)
Explanation: The missing quantity is the steric factor \(P\). It accounts for the fraction of collisions having the required orientation. The factor \(Z\) represents collision frequency, while the exponential term accounts for sufficient energy. Thus, \(k=PZe^{-E_a/(RT)}\). Omitting \(P\) would incorrectly treat every energetic collision as geometrically successful.
404. The collision-theory parameters are \(Z=2.0\times10^{10}\,s^{-1}\), \(P=0.020\), and \(e^{-E_a/(RT)}=5.0\times10^{-4}\). The predicted rate constant is:
ⓐ. \(2.0\times10^{3}\,s^{-1}\)
ⓑ. \(2.0\times10^{5}\,s^{-1}\)
ⓒ. \(5.0\times10^{7}\,s^{-1}\)
ⓓ. \(2.0\times10^{8}\,s^{-1}\)
Correct Answer: \(2.0\times10^{5}\,s^{-1}\)
Explanation: \( \textbf{Collision-theory expression:} \)
Use:
\[
k=PZe^{-E_a/(RT)}
\]
Substitute the steric factor:
\[
P=0.020
\]
Substitute the collision frequency:
\[
Z=2.0\times10^{10}\,s^{-1}
\]
Substitute the energetic fraction:
\[
e^{-E_a/(RT)}=5.0\times10^{-4}
\]
\( \textbf{Combined-factor result:} \)
Therefore:
\[
k=(0.020)(2.0\times10^{10})(5.0\times10^{-4})
\]
First combine the numerical factors:
\[
(0.020)(5.0\times10^{-4})=1.0\times10^{-5}
\]
Hence:
\[
k=(2.0\times10^{10})(1.0\times10^{-5})
\]
\[
k=2.0\times10^{5}\,s^{-1}
\]
Both energy and orientation reduce the rate constant far below the raw collision frequency.
405. Assertion: A steric factor smaller than \(1\) indicates that not all sufficiently energetic collisions lead to reaction.
Reason: Some energetic collisions occur with an unsuitable orientation.
ⓐ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓑ. Assertion is true, but Reason is false
ⓒ. Assertion is false, but Reason is true
ⓓ. Both Assertion and Reason are true, and Reason explains Assertion
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: The steric factor measures the orientational success fraction in the simplified collision model. A value below \(1\) means that only part of the energetic collision population is properly aligned. Molecules may collide through non-reactive regions or in geometries that do not permit the required bond rearrangement. Such collisions possess enough energy but still fail to form products. The Reason directly explains the meaning of the reduced steric factor.
406. Consider the following statements about the steric factor \(P\).
Statement I: It accounts for molecular orientation during collisions.
Statement II: In the simplest interpretation, it commonly lies between \(0\) and \(1\).
Statement III: It is identical to the activation energy of the reaction.
The valid statements are:
ⓐ. I and III only
ⓑ. II and III only
ⓒ. I and II only
ⓓ. I, II and III
Correct Answer: I and II only
Explanation: The steric factor represents the fraction of collisions with favourable geometry. As a fraction in the simple collision picture, it is commonly between \(0\) and \(1\). Activation energy is an energy barrier measured in units such as \(kJ\,mol^{-1}\). The steric factor is dimensionless and conceptually distinct from \(E_a\). Statement III therefore confuses orientation with energetic requirement.
407. Despite a very high collision frequency, a reaction proceeds slowly at a fixed temperature. Which combination best explains the observation within collision theory?
ⓐ. A small energetic fraction and a small steric factor
ⓑ. A zero collision frequency and a steric factor of \(1\)
ⓒ. A low activation energy and a large steric factor
ⓓ. An energetic fraction of \(1\) and perfectly favourable orientation
Correct Answer: A small energetic fraction and a small steric factor
Explanation: A high total collision frequency alone does not guarantee a high reaction rate. If \(E_a\) is large relative to \(RT\), only a small fraction of collisions has sufficient energy. If the molecular geometry is restrictive, only a small fraction of those energetic collisions is favourably oriented. Since \(k=PZe^{-E_a/(RT)}\), both small factors can strongly reduce \(k\) despite a large \(Z\). The slow reaction therefore reflects ineffective rather than infrequent encounters.
408. On a molecular-energy distribution graph, the fraction of molecules having energy sufficient for reaction is represented by:
ⓐ. the area under the curve to the right of \(E_a\)
ⓑ. the height of the curve exactly at \(E_a\)
ⓒ. the area under the curve to the left of \(E_a\)
ⓓ. the horizontal distance from zero energy to the curve maximum
Correct Answer: the area under the curve to the right of \(E_a\)
Explanation: The activation energy marks the minimum energy required for the reaction pathway. Molecules with energy below this value do not satisfy the energetic condition. The relevant fraction therefore consists of molecules whose energies are equal to or greater than \(E_a\). On the graph, these molecules occupy the area to the right of the activation-energy line. The height at a single energy does not represent the complete energetic population.
409. A molecular-energy distribution curve is normalised so that the total area beneath it equals (1). This total area represents:
ⓐ. the activation energy required by the reaction
ⓑ. the complete molecular population expressed as a fraction
ⓒ. the fraction of molecules undergoing effective collisions
ⓓ. the numerical value of the reaction rate constant
Correct Answer: the complete molecular population expressed as a fraction
Explanation: Each small area beneath a molecular-energy distribution curve represents the fraction of molecules having energies within a particular interval. Adding the areas over all possible molecular energies accounts for the entire population. Because the curve is normalised, this complete population is represented by a total area of (1), equivalent to (100%). The activation energy is shown separately as an energy threshold and is not obtained from the total area. Only the portion of the curve beyond the activation-energy threshold represents molecules satisfying the energy requirement for reaction. Temperature changes the distribution of molecules among energy intervals but does not change the total normalised area.
410. A normalised molecular-energy distribution curve has molecular energy on the horizontal axis and a total area of \(1\). A vertical line marks the activation energy \(E_a\). The area beneath the curve to the right of this line represents:
ⓐ. the fraction of molecules having \(E\ge E_a\)
ⓑ. the fraction of molecules having \(E\lt E_a\)
ⓒ. the value of the activation energy itself
ⓓ. the average energy of the molecular population
Correct Answer: the fraction of molecules having \(E\ge E_a\)
Explanation: The activation energy \(E_a\) is the minimum energy required for molecules to cross the energy barrier associated with the reaction pathway. Molecules lying to the left of the \(E_a\) line have energies below this threshold. Molecules lying on or to the right of the line satisfy the energetic requirement. Since the distribution is normalised, the area of this region directly gives the fraction of molecules having \(E\ge E_a\). The height of the curve at one energy value would describe only the distribution at that particular energy, not the complete energetic fraction. A favourable molecular orientation may still be required even after the energy condition is satisfied.
411. Two energy-distribution curves P and Q correspond to the same gas sample at different temperatures. Curve Q has a lower maximum, is broader, and is shifted toward higher energy. Which comparison is correct?
ⓐ. \(T_Q\lt T_P\)
ⓑ. \(T_Q=T_P\)
ⓒ. \(T_Q\gt T_P\)
ⓓ. Temperature cannot be inferred from the curve shapes
Correct Answer: \(T_Q\gt T_P\)
Explanation: A higher-temperature distribution is broader because molecular energies are spread over a larger range. Its peak becomes lower because the same total area is distributed more widely. The curve also extends farther into the high-energy region. These are the features described for curve Q. Therefore, Q corresponds to the higher temperature.
412. Assertion: Raising the temperature can produce a large increase in reaction rate even when the average molecular energy increases only moderately.
Reason: The fraction of molecules lying beyond the activation-energy threshold can increase substantially.
ⓐ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓑ. Assertion is true, but Reason is false
ⓒ. Assertion is false, but Reason is true
ⓓ. Both Assertion and Reason are true, and Reason explains Assertion
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: Reaction rate depends strongly on the population of molecules capable of crossing the activation barrier. Increasing temperature broadens the energy distribution and enlarges its high-energy tail. Even a moderate shift in molecular energies can move many more molecules beyond \(E_a\). This produces a disproportionately large increase in effective collisions. The Reason therefore explains the strong temperature sensitivity stated in the Assertion.
413. A catalyst is added to a reaction mixture without changing its temperature. On a molecular-energy distribution graph, the immediate effect is best represented by:
ⓐ. shifting the entire distribution curve toward higher energy
ⓑ. increasing the total area under the curve
ⓒ. moving the activation-energy threshold toward lower energy
ⓓ. making all molecules possess the same energy
Correct Answer: moving the activation-energy threshold toward lower energy
Explanation: At unchanged temperature, the distribution of molecular energies remains essentially the same. A catalyst changes the reaction pathway rather than directly heating the molecules. The alternative pathway has a lower activation energy. On the graph, the \(E_a\) line therefore moves to the left. The area beyond the new threshold is larger, so more molecules can react successfully.
414. Match each change in Column I with its effect in Column II.
| Column I | Column II |
|---|
| P. Increase in temperature | 1. Activation-energy line shifts left |
| Q. Addition of a catalyst at fixed temperature | 2. Distribution becomes broader with a lower peak |
| R. Increase in activation energy at fixed temperature | 3. Smaller area lies beyond the threshold |
| S. Normalising the distribution | 4. Total area becomes \(1\) |
ⓐ. P-1, Q-2, R-4, S-3
ⓑ. P-2, Q-1, R-3, S-4
ⓒ. P-2, Q-3, R-1, S-4
ⓓ. P-4, Q-1, R-3, S-2
Correct Answer: P-2, Q-1, R-3, S-4
Explanation: Increasing temperature broadens the distribution and lowers its peak, so P matches 2. A catalyst lowers the activation energy and shifts the threshold left, so Q matches 1. Raising the barrier at fixed temperature leaves fewer molecules beyond it, giving R-3. A normalised distribution represents the complete population with total area \(1\), giving S-4. These effects distinguish changes in molecular energies from changes in the reaction pathway.
415. At temperature \(T_1\), \(2\%\) of molecules have energy at least equal to \(E_a\). At a higher temperature \(T_2\), this fraction becomes \(8\%\). If collision frequency and orientation factor are assumed unchanged, the energetic contribution to the rate increases by a factor of:
ⓐ. \(2\)
ⓑ. \(3\)
ⓒ. \(4\)
ⓓ. \(6\)
Correct Answer: \(4\)
Explanation: The original energetic fraction is:
\[
f_1=2\%=0.02
\]
The higher-temperature fraction is:
\[
f_2=8\%=0.08
\]
The multiplication factor is:
\[
\frac{f_2}{f_1}
=
\frac{0.08}{0.02}
\]
\[
\frac{f_2}{f_1}=4
\]
Thus, the number of energetically qualified collisions becomes four times larger under the stated assumptions.
416. Consider the following statements about molecular-energy distributions.
Statement I: At any non-zero temperature, molecules do not all possess the same kinetic energy.
Statement II: Increasing temperature increases the area under the normalised curve.
Statement III: Increasing temperature increases the fraction of molecules with energy above a fixed \(E_a\).
The valid statements are:
ⓐ. I, II and III
ⓑ. I and II only
ⓒ. II and III only
ⓓ. I and III only
Correct Answer: I and III only
Explanation: Molecular collisions continually redistribute energy, so a sample contains molecules with a range of kinetic energies. Raising temperature shifts more of the population into higher-energy regions. Consequently, the fraction beyond a fixed activation threshold increases. The total area of a normalised curve remains \(1\), because the total molecular fraction remains \(100\%\). Statement II is therefore incorrect.
417. The peak of a molecular-energy distribution curve does not directly represent:
ⓐ. the energy possessed by the largest number of molecules
ⓑ. the most probable molecular energy
ⓒ. the activation energy for every reaction
ⓓ. a value that shifts when temperature changes
Correct Answer: the activation energy for every reaction
Explanation: The curve maximum identifies the most probable energy of the molecular population. It depends on the temperature of the sample. Activation energy, however, belongs to a particular reaction pathway. Different reactions involving the same molecules can have different activation barriers. The distribution peak and the activation-energy threshold are therefore separate concepts.
418. Which observation is not explained adequately by the simplest collision theory alone?
ⓐ. Increasing gas concentration increases collision frequency
ⓑ. A multistep solution reaction with solvent stabilisation
ⓒ. Energetic collisions are more common at higher temperature
ⓓ. Unfavourable orientation can prevent reaction
Correct Answer: A multistep solution reaction with solvent stabilisation
Explanation: Simple collision theory is most directly suited to elementary gas-phase encounters. A solution-phase reaction may involve solvation, diffusion, solvent reorganisation, and several intermediates. These effects are not described fully by counting hard-sphere collisions and applying energy and orientation factors. The theory can still provide qualitative insight, but it is not a complete molecular model for such a mechanism. More detailed kinetic or transition-state treatments are required.
419. Assertion: Collision theory is more successful qualitatively than quantitatively for many complex reactions.
Reason: Real molecules may have complicated energy redistribution, intermolecular forces, and multistep pathways.
ⓐ. Both Assertion and Reason are true, and Reason explains Assertion
ⓑ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓒ. Assertion is true, but Reason is false
ⓓ. Assertion is false, but Reason is true
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: Collision theory correctly highlights the importance of encounter frequency, activation energy, and orientation. Complex molecules, however, do not always behave as simple rigid spheres. Internal vibrations, solvent effects, attractive forces, and intermediate formation can affect the rate. These features make precise quantitative prediction difficult using the simplest model. The Reason therefore explains the limitation stated in the Assertion.
420. A reaction proceeds through three elementary steps and contains two detectable intermediates. Why can a single-collision description be inadequate?
ⓐ. The observed rate may depend on the sequence and relative rates of several elementary events
ⓑ. Each elementary step loses its activation barrier after the first intermediate is formed
ⓒ. Detectable intermediates prevent further collisions between the original reactant molecules
ⓓ. All elementary steps must have the same rate constant for the overall process to occur
Correct Answer: The observed rate may depend on the sequence and relative rates of several elementary events
Explanation: A multistep mechanism contains several transition states and intermediate species. The overall rate may be controlled mainly by one slow step or by a combination of steps. A single encounter between the original reactants does not describe the entire pathway. Intermediate concentrations and step-specific rate constants may influence the observed law. Mechanistic analysis is therefore needed in addition to simple collision counting.
