Question

Choose the correct expression regarding average rate of reaction $\left(r_{avg.}\right)$ and instantaneous rate of reaction $\left(r_{inst.}\right)$:

• A. $r_{inst.}=\underset{\Delta t\to 0}{lim}\left(r_{avg.}\right)$
• B. $r_{avg.}=\underset{\Delta t\to 0}{lim}\left(r_{inst.}\right)$
• C. $r_{avg.}=\underset{\Delta C\to 0}{lim}\left(r_{inst.}\right)$
• D. $r_{inst.}=\underset{\Delta C\to 0}{lim}\left(r_{avg.}\right)$

Answer 1

The correct option is A $r_{inst.}=\underset{\Delta t\to 0}{lim}\left(r_{avg.}\right)$

Average rate of reaction:
For a reaction,
$A\to B$
$\text{Average rate}=\frac{\text{Total change in concentration}}{\text{Total time taken}}$

$\text{Average rate}=\frac{\Delta C}{\Delta t}$
Instantaneous rate of a reaction:
Rate of reaction at a particular instant is called Instantaneous rate of a reaction.
For a reaction
$A\to B$
$r_{inst.}=\frac{dC}{dt}$
$r_{\text{inst.}}=\underset{\Delta t\to 0}{lim}\left(\frac{\Delta C}{\Delta t}\right)=\frac{dC}{dt}$
So,
$r_{inst.}=\underset{\Delta t\to 0}{lim}\left(r_{avg.}\right)$