Question

Match the graph given in Column I with the order of reaction given in Column II. More than one item in Column I may link to the same item of Column II.

Column I		Column II
A		1	First order
B		2	Zero order
C
D

• A. $A-(1), B-(2), C-(2), D-(1)$
• B. $A-(2), B-(2), C-(1), D-(1)$
• C. $A-(2), B-(1), C-(1), D-(2)$
• D. $A-(1), B-(1), C-(2), D-(2)$

Answer 1

Answer: (A)

$A. \rightarrow(1)\,\, B. \rightarrow(2)\,\, C. \rightarrow(2)\,\, D. \rightarrow(1)$
For zero order reaction rate equation may be written as
$[R]=-k t+\left[R_{0}\right]$ ...(i)
Which denotes a straight line equation similar to $y=m x+ c$
On transforming (i) $\frac{[R]-\left[R_{0}\right]}{t}=-k$
$k=\frac{\left[R_{0}\right]-[R]}{t}$

$k=$ Rate
Rate $=k \cdot[t]^{0}$
$\Rightarrow$ Rate $\propto[t]^{0}$

For a first order reaction $\frac{d x}{d t} \propto$ [concentration]
$\therefore$ Graph between rate and concentration may be drawn as
$k=\frac{2.303}{t} \log \frac{[R]_{0}}{[R]}$
$\frac{k t}{2.303}=\log \left[\frac{R^{\circ}}{R}\right]$
or $\frac{k t}{2.303}=\log [R]_{0}-\log [R]$
$\log [R]=\underset{\text { Slope }}{\left(\frac{-k}{2.303}\right)} t+\underset{\text { Intercept }}{\log [R]_{0}}$