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Multiple choice chemistry chemical reactions and equations kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

The rate constant for the reaction $2{N} _{2}{O} _{5}\rightarrow 4{N}{O} _{2}+{O} _{2}$, is $3.0\times 10^{-5}\sec^{-1}$. lf the rate is $2.40\times 10^{-5}$ mol litre $sec^{-1}$ then, the concentration of ${N} _{2}{O} _{5} ($in mol $litre^{-1})$ is:

  1. 1.4

  2. 1.2

  3. 0.04

  4. 0.8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rate constant $= 3 \times 10^{-5} sec^{-1}$


So, from it's unit it is clear that, it is a first order reaction.


For first order reaction the expression will be:
Rate $= K [N _{2}O _{5}]$
$[N _{2}O _{5}] = \dfrac{2.40 \times 10^{-5}}{3 \times 10^{-5}}$$=\dfrac{2.40}{3} = 0.8$

Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

For which of the following reactions the molecularity and orders of the reaction are two and two respectively:

  1. ester hydrolysis in acid medium.

  2. inversion of cane sugar in acid aqueous solution.

  3. hydrolysis of ethyl acetate in caustic soda aqueous solution.

  4. decomposition hydrogen peroxide in acid solution.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The hydrolysis of ethyl acetate in caustic soda aqueous solution is represented by the following reaction.
$CH _{3}COOC _{2}H _{5}+NaOH\rightarrow  CH _{3}COONa+C _{2}H _{5}OH$
The expression for the rate of the reaction is $r=k[CH _{3}COOC _{2}H _{5}][NaOH].$
The overall order of the reaction is 2 and it is a bimolecular reaction.

Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

The rate constant, $\mathrm{k}$ for the reaction $\displaystyle \mathrm{N} _{2}\mathrm{O} _{5}(\mathrm{g})\rightarrow 2\mathrm{N}\mathrm{O} _{2}(\mathrm{g})+\frac{1}{2}\mathrm{O} _{2}(\mathrm{g})$ ls $2.3\times 10^{-2}\mathrm{s}^{-1}$. Which equation given below describes the change of $[\mathrm{N} _{2}\mathrm{O} _{5}]$ with time?

$[\mathrm{N} _{2}\mathrm{O} _{5}] _{0}$ and $[\mathrm{N} _{2}\mathrm{O} _{5}] _{\mathrm{t}}$ correspond to concentration of $\mathrm{N} _{2}\mathrm{O} _{5}$ initially and at time $\mathrm{t}$.

  1. $[N _{2}O _{5}] _{t}=[N _{2}O _{5}] _{0}+kt$
  2. $[N _{2}O _{5}] _{0}=[N _{2}O _{5}] _{t}e^{kt}$
  3. $log _{10}[N _{2}O _{5}] _{t}=log _{10}[N _{2}O _{5}] _{0}-kt$
  4. $ln\dfrac{[N _{2}O _{5}] _{0}}{[N _{2}O _{5}] _{t}}=kt$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The decomposition of  $\mathrm{N} _{2}\mathrm{O} _{5}$ follows first order kinetics.


The integrated rate law expression is $ln\dfrac{[N _{2}O _{5}] _{0}}{[N _{2}O _{5}] _{t}}=kt$.

It can also be represented as $log _{10}[N _{2}O _{5}] _{t}=log _{10}[N _{2}O _{5}] _{0}-\dfrac {kt} {2.303}.$


It can also be represented as $[N _{2}O _{5}] _{t}=[N _{2}O _{5}] _{0}e^{-kt}.$

Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions
For the reaction ; $2H _2O _2(aq)\rightarrow 2H _2O(l)+O _2(g)$, rate of decomposition for $H _2O _2=k[H _2O _2]^2$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For $2H _2O _2(aq)\rightarrow 2H _2O(l)+O _2(g)$ rate of decomposition for $H _2O _2=k[H _2O _2]$. It is a first order reaction.  It proceeds through following mechanism.

$\displaystyle H _2O _2 \xrightarrow {slow} H _2O + O $

$\displaystyle  O + O \xrightarrow {fast} O _2$

Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

For the reaction; $2N _2O _5\rightarrow 4NO _2+O _2$, rate and rate constant are $1.02\times 10^{-4} M sec^{-1}$ and $3.4\times 10^{-5}  sec^{-1}$ respectively, then concentration of $N _2O _5$, at that time will be:

  1. $1.732\ M$
  2. $3\ M$
  3. $1.02\times 10^{-4} M$
  4. $3.5\times 10^{5} M$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
From the unit of rate constant we can identify the reaction as first order.

As we know,
$r=K[N _2O _5]$

$\therefore [N _2O _5]=\frac {r}{K}=\frac {1.02\times 10^{-4}}{3.4\times 10^{-5}}=3M$.
Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

For the first order reaction:-
$2N _2O _5(g)\rightarrow 4NO _2(g)+O _2(g)$

  1. the concentration of the reactant decreases exponentially with time

  2. the half-life of the reaction decreases with increasing temperature

  3. the half-life of the reaction depends on the initial concentration of the reactant

  4. the reaction proceeds to 99.6% completion in eight half-life duration
Reveal answer Fill a bubble to check yourself
A,B,D Correct answer
Explanation

Option (A),(B),(D) are correct.
(C) : The half-life of the reaction is independent of the initial concentration of the reactant. Half-life for first order reaction is :$t _{1/2} = 0.693/k$
A first-order reaction has a rate proportional to the concentration of one reactant.
First-order rate constants have units of $sec^{-1}$. In other words, a first-order reaction has a rate law in which the sum of the exponents is equal to 1. 

Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

The reaction; $N _2O _5(g) \longrightarrow 2NO _2(g)+\frac {1}{2}O _2(g)$ is of first order for $N _2O _5$ with rate constant $6.2\times 10^{-4}s^{-1}$. What is the value of rate of reaction when $[N _2O _5]=1.25 \ mol L^{-1}$?

  1. $5.15\times 10^{-5}mol L^{-1}s^{-1}$
  2. $6.35\times 10^{-3}mol L^{-1}s^{-1}$
  3. $7.75\times 10^{-4}mol L^{-1}s^{-1}$
  4. $3.85\times 10^{-4}mol L^{-1}s^{-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

As we know,
$r=K[N _2O _5]=6.2\times 10^{-4}\times 1.25=7.75\times 10^{-4} mol L^{-1} s^{-1}$.

Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

The concentration of acetate ions in $1 M$ acetic acid $(K _{a} = 2 \times 10^{-5})$ solution containing $0.1 M - HCl$ is

  1. $2 \times 10^{-1}$
  2. $2 \times 10^{-3}$
  3. $2 \times 10^{-4}$
  4. $4.4 \times 10^{-3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the presence of a strong acid (HCl), the dissociation of acetic acid is suppressed by the common ion effect. The concentration of H+ is dominated by HCl (0.1 M). Ka = [H+][CH3COO-] / [CH3COOH]. 2e-5 = (0.1 * [CH3COO-]) / 1.0. Thus, [CH3COO-] = 2e-4 M.

Multiple choice chemistry chemical kinetics kinetic study of some first order reactions rate of chemical reaction endothermic and exothermic reactions

The hydrolysis of an ester was carried out with 0.1 M $H _2SO _4$ and 0.1 M HCl separately. Which of the following expressions between the rate consists is expected? The rate expression being rate = $k[H^{\oplus}][ester]$ 

  1. $k _{HCl}\, =\, k _{H _2SO _4}$
  2. $k _{HCl}\, >\, k _{H _2SO _4}$
  3. $k _{HCl}\, <\, k _{H _2SO _4}$
  4. $k _{ H _2SO _4}\, =\, k _{HCl}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$[H _2SO _4]\, =\, 0.1\, M\, =\, 0.1\, \times\, 2\, =\, 0.2 N$

$[HCl]$ = $0.1 N$

In case of $[H _2SO _4]$ 

$r _1\, =\, k[H^{\oplus}][Ester]$ 

$\displaystyle k _{H _2SO _4}\, = \frac{r _1}{2\, N\, \times\, [Ester]}$ 

In case of HCl, $r _1\, =\, k[H^{\oplus}]\, [Ester]$ 

$\displaystyle k _{HCl}\, =\, \frac{r _2}{1\, N\, [Ester]}$ 

Hence $K _{HCl}\, >\, K _{H _2SO _4}$