1

### NEET 2016 Phase 1

The rate of first-order reaction is 0.04 mol L$-$1 s$-$1 at 10 seconds and 0.03 mol L$-$1 s$-$1 at 20 seconds after initiation of the reaction. The half-life period of the reaction is
A
44.1 s
B
54.1 s
C
24.1 s
D
34.1 s

## Explanation

For the first order reaction

A $\to$ Product

Rate $\propto$ [A]

k = ${{2.303} \over {{t_2} - {t_1}}}\log {{{{\left( {rate} \right)}_1}} \over {{{\left( {rate} \right)}_2}}}$

= ${{2.303} \over {20 - 10}}\log {{0.04} \over {0.03}}$

= 0.0287 sec-1

${t_{{1 \over 2}}} = {{0.693} \over k} = {{0.693} \over {0.0287}}$ = 24.14 sec
2

### AIPMT 2015 Cancelled Paper

The activation energy of a reaction can be determined from the slope of which of the following graphs?
A
ln k vs. ${1 \over T}$
B
${T \over {\ln \,k}}$ vs. ${1 \over T}$
C
ln k vs. $T$
D
${{\ln k} \over T}$ vs. $T$

## Explanation

According to Arrhenius equation,

$k = A{e^{ - {{{E_a}} \over {ET}}}}$

Taking natural log on both the sides we get,

ln k = ln A ${ - {{{E_a}} \over {ET}}}$ ...........(1)

Comparing (1) with standard form of equation of line

y = mx + C

We get Slope, m = ${ - {{{E_a}} \over R}}$

Hence, if ln k is plotted against 1/T, slope of the line will be ${ - {{{E_a}} \over R}}$.
3

### AIPMT 2015 Cancelled Paper

When initial concentration of a reactant is doubled in a reaction, its half-life period is not affected. The order of the reaction is
A
second
B
more than zero but less than first
C
zero
D
first.

## Explanation

Half-life period of a first order reaction is independent of initial concentration,

${t_{{1 \over 2}}} = {{0.693} \over k}$
4

### AIPMT 2015

The rate constant of the reaction A $\to$ B is 0.6 $\times$ 10$-$3 mol L$-$1 s$-$1. If the concentration of A is 5 M, then concentration of B after 20 minutes is
A
3.60 M
B
0.36 M
C
0.72 M
D
1.08 M

## Explanation

For zero order reaction unit of rate constant is mole per second.

$\therefore$ For zero order

x = kt

$\Rightarrow$ x = 0.6 × 10–3 × 20 × 60 = 0.72 M