Think of a brand new tool. At the moment you start using it (\( t = 0 \)), it's at its full potential (activity = 1). As you use it over time, it might become less effective (activity \(<\) 1) due to wear and tear or other factors.
Step 1: Understand the concept of catalyst activity.
Catalyst activity refers to the rate at which a catalyst can accelerate a chemical reaction. It is often quantified as the number of moles of reactant converted per unit time per unit mass of catalyst under specific reaction conditions.
Step 2: Consider the state of the catalyst at time \( t = 0 \).
At the very beginning of a reaction, \( t = 0 \), the catalyst is assumed to be in its initial, fresh state, ready to promote the reaction. It has not yet undergone any deactivation processes such as poisoning, fouling, or sintering, which can reduce its effectiveness over time.
Step 3: Define the initial activity of a catalyst.
The activity of a fresh, unused catalyst is typically taken as a reference point. To normalize the activity over time as the catalyst deactivates, the initial activity is often defined as unity (1). This means that at \( t = 0 \), the catalyst is considered to be 100\% active.
Step 4: Evaluate the given options.
Option 1 (Unity): This aligns with the convention that the initial activity of a catalyst at \( t = 0 \) is defined as 1.
Option 2 (Infinity): A catalyst cannot have infinite activity.
Option 3 (Zero): At \( t = 0 \), the catalyst is fresh and has its maximum initial activity, which is not zero.
Option 4 (Negative): Catalyst activity is a positive quantity representing the rate of reaction enhancement.
Step 5: Select the correct answer.
The activity of a catalyst at time \( t = 0 \) is unity, representing its initial, undegraded state.
Arrange the following compounds in increasing order of their reactivity towards \( S_N2 \) displacement: 2-Bromo-2-methylbutane, 1-Bromopentane, 2-Bromopentane.
In the following pair of halogen compounds, which compound undergoes \( S_N1 \) reaction faster and why?
Assertion (A): Aromatic primary amines cannot be prepared by Gabriel Phthalimide synthesis.
Reason (R): Aryl halides do not undergo nucleophilic substitution reaction with the anion formed by phthalimide.
The representation of octal number \((532.2){_8}\) in decimal is ____ .
Given the signal,
\(X(t) = cos t\), if \(t<0 \)
\(Sin\ t\), if \(t\ge0 \)
The correct statement among the following is?
A linear system at rest is subject to an input signal \(r(t) = 1 - e^{-t}\). The response of the system for t>0 is given by \(c(t) = 1 - e^{-2t}\). The transfer function of the system is:
In the given circuit below, voltage \(V_C(t)\) is: