Tag: rate of chemical reaction

Questions Related to rate of chemical reaction

The hydrolysis of ethyl acetate in an acidic medium is a:

  1. zero order reaction

  2. first order reaction

  3. pseudo first order reaction

  4. second order reaction


Correct Option: B
Explanation:
$1.$ Decomposition of $H _2O _2$ in aqueous solution.
$H _2O _2\rightarrow H _2O+1/2O _2$
$2.$ Hydrolysis of methyl acetate in the presence of mineral acids.
$CH _3COOCH _3 +H _2O\rightarrow CH _3COOH+CH _3OH$
$3.$ Inversion of cane sugar in the presence of mineral acids.
$C _{12}H _{22}O _{11}+H _2O\xrightarrow {[H^+]}C _6H _{12}O _6+C _6H _{12}O _6$
$4.$ Decomposition of ammonium nitrate in aqueous solution.
$NH _4NO _2\rightarrow N _2+2H _2O$
$5.$ Hydrolysis of diazo derivatives.
$C _5H _5N+NCl + H _2O\rightarrow C _6H _5OH+N _2+HCl$
FIRST ORDER REACTION : When the rate of reaction depends only on one concentration term of reactant. A first order reaction is one whose rate varies as first power of the concentration of the reactant, i.e. the rate increases as number of times as the concentration of reactant is increased.
Examples are given above:

The reaction $2N _2O _5(g)\, \rightarrow\, 4NO _2(g)\, +\, O _2(g)$ is first order w.r.t. $N _2O _5$. Which of the following graphs would yield a straight line ?

  1. $log\, p _{N _2O _5}$ vs time with -ve slope

  2. $(p _{N _2O _5})^{-1}$ vs time

  3. $p _{N _2O _5}$ vs time

  4. $log\, p _{N _2O _5}$ vs time with +ve slope


Correct Option: A
Explanation:

For a first order reaction, the graph of logarithm of the partial pressure of reactant to the time is a straight line with negative slope. 


Hence, $\displaystyle log\, p _{N _2O _5}$ vs time t will give a straight line.

When ethyl acetate was hydrolyzed in the presence of $0.1 M$ $HCl$, the constant was found to be $5.40\, \times\, 10^{-5}\, s^{-1}$. But when $0.1$ $M\, H _2SO _4$ was used for hydrolysis, the rate constant was found to be $6.20\, \times\,10^{-5}\, s^{-1}$. From these we can say that:

  1. $H _2SO _4$ is stronger than $HCl.$

  2. $H _2SO _4$ and $HCl$ are both of the same strength.

  3. $H _2SO _4$ is weaker than $HCl.$

  4. The data is insufficient to compare the strength of $HCl$ ad $H _2SO _4$.


Correct Option: A
Explanation:

Since $k _{H _2SO _4}\, >\, k _{HCl},$ hence $H _2SO _4$ is stronger acid than HCl.

For the reaction $2N _2O _5\, \rightarrow\, 4NO _2\, +\, O _2$, if $\displaystyle -\, \frac{d[N _2O _5]}{dt}\, =\, k _1[N _2O _5]$, $\displaystyle \frac{d[NO _2]}{dt}\, =\, k _2[N _2O _5]$, $\displaystyle \frac{d[O _2]}{dt}\, =\, k _3[N _2O _5]$.
What is the relation between $k _1, k _2$ and $k _3$?

  1. $k _1\, =\, k _2\, =\, k _3$

  2. $2k _1\, =\, k _2\, =\, 4k _3$

  3. $2k _1\ =\, 4k _2\, =\, k _3$

  4. None of the above


Correct Option: B
Explanation:

As we know, for a reaction: $2N _2O _5\, \rightarrow\, 4NO _2\, +\, O _2$

$\displaystyle -\, \frac{1}{2}\, \frac{d[N _2O _5]}{dt}\, =\, \frac{1}{4}\, \frac{d[NO _2]}{dt}\, =\, \frac{d[O _2]}{dt}$

So, $2k _1\, =\, k _2\, =\, 4k _3.$

The rate law for the reaction : $:Ester+H^+\rightarrow Acid+Alcohol\,$ is
$V\,=\,k\;\left[ester \right]\;\left[H _3O^+ \right]^0$
What would be the new rate if
(a)$\;$conc. of ester is doubled
(b)$\;$conc. of $:H^{+}$ is doubled

  1.  (a)$\;v\;$ (b)$\;2v$

  2.  (a)$\;2v\;$ (b)$\;v$

  3.  (a)$\;2v\;$ (b)$\;2v$

  4. None of the above 


Correct Option: B
Explanation:

$\upsilon=k[ester][H _3O^+]$


(a) Conc. of ester is doubled rate also double that is $2\upsilon$ because rate of the reaction depends upon ester concentration.

(b) Conc. of $H^+$ is doubled rate does not change that is $\upsilon$ because rate of the reaction does not depends on $H _3O^+$ concentration.

So answer is B.

In the presence of acid, the initial concentration of cane-sugar was reduced from 0.2 M to 0.1 in 5 hr and to 0.05 M in 10 hr. The reaction must be of :

  1. Zero order

  2. First order

  3. Second order

  4. Fractional order


Correct Option: B
Explanation:

$\displaystyle 0.2\, M \underset{t _{1/2}\, =\, 5hr}{\rightarrow} 0.1\, M \underset{t _{1/2}\, =\, 5hr}{\rightarrow} 0.05\, M$

$From\, 0.2\, M \underset{t\, =\, 10hr}{\rightarrow}\, 0.05\, M$
So $t _{1/2}$ is constant which is characteristic of first order reaction.
Hence, $t _{1/2}\, \propto\, (a)^0$.

The decomposition of $H _2O _2$ can be followed by titration with $KMnO _4$ and is found to be a first order reaction. The rate constant is $4.5\, \times\, 10^{-2}$. In an experiment, the initial titrate value was 25 mL. The titrate value will be 5 mL after a lapse of :

  1. $4.5\, \times\, 10^{-2}\, \times\, 5\, min$

  2. $\displaystyle \frac{log _{e}5}{4.5\, \times\, 10^{-2}}\, min$

  3. $\displaystyle \frac{log _{e}5/4}{4.5\, \times\, 10^{-2}}\, min$

  4. None of the above


Correct Option: B
Explanation:

As we know,
$\displaystyle t\, =\, \frac{2.303}{k}\, log\, \frac{V _0}{V _1}$

$\displaystyle =\, \frac{1}{k}\, ln\, \frac{V _0)}{V _1}$

$\displaystyle =\, \frac{1}{4.5\, \times\, 10^{-2}\, min^{-1}}\, In\, \frac{25mL}{5mL}$

$\displaystyle =\, \frac{log _{e}5}{4.5\, \times\, 10^{-2}}min$ 

The half-life of decomposition of $N _2O _5$ is a first order reaction represented by:


$N _2O _5\rightarrow N _2O _4+1/2O _2$

After 15 minutes, the volume of $O _2$ produced is 9 $mL$ and at the end of the reaction is 35 $mL$. The rate constant is equal to:

  1. $\;\displaystyle\frac{1}{15}log _e\displaystyle\frac{35}{26}$

  2. $\;\displaystyle\frac{1}{15}log _e\displaystyle\frac{44}{26}$

  3. $\;\displaystyle\frac{1}{15}log _e\displaystyle\frac{35}{36}$

  4. None of the above 


Correct Option: A
Explanation:

For a first order reaction,

$KT= ln (a/a-x)$

So, for the following reaction:

$N _2O _5\rightarrow N _2O _4+1/2O _2$

$K\times15\,=\,ln\begin{pmatrix}\displaystyle\frac{35-0}{35-9}\end{pmatrix}$


$N _2O _5\rightarrow N _2O _4+1/2O _2$

$K= \dfrac{1}{15} \,ln\begin{pmatrix}\displaystyle\frac{35}{26}\end{pmatrix}$

The reaction $N _{2}O _{5}$ (in $CCl _{4}$) $\rightarrow 2NO _{2}+1/2O _{2}(g)$ is the first order in $N _{2}O _{5}$ with rate constant $6.2\times 10^{-4}S^{-1}$. 


What is the value of the rate of reaction when $N _2O _5=1.25:mole:L^{-1}$ ?

  1. $7.75\times 10^{-4}mol:L^{-1}S^{-1}$

  2. $6.35\times 10^{-3}mol:L^{-1}S^{-1}$

  3. $5.15\times 10^{-5}mol:L^{-1}S^{-1}$

  4. $3.85\times 10^{-4}mol:L^{-1}S^{-1}$


Correct Option: A
Explanation:
For the first-order reaction, the rate of the reaction is given by the expression

Rate $\displaystyle  = k [N _2O _5]$ where k is the rate constant.

Substitute values in the above expression

Rate $\displaystyle  = 6.2\times 10^{-4}S^{-1} \times 1.25\:mole\:L^{-1} = 7.75\times 10^{-4}mol\:L^{-1}S^{-1}$

So, the correct option is $A$

The half life of decomposition of $N _2O _5$ is a first order reaction represented by
$N _2O _5\, \rightarrow\, N _2O _4\, =\, 1/2O _2$
After 15 min the volume of $O _2$ produced is $9mL$ and at the end of the reaction $35 mL$. The rate constant is equal to :

  1. $\displaystyle \frac{1}{15}\, log\frac{35}{26}$

  2. $\displaystyle \frac{1}{15}\log\frac{44}{26}$

  3. $\displaystyle \frac{1}{15}\, log\frac{35}{36}$

  4. None of the above 


Correct Option: A
Explanation:

$\displaystyle k\, =\, \frac{2.303}{t}\, log\, \frac{V _{\infty}}{V _{\infty}\, -\, V _t}$

$\displaystyle =\, \frac{1}{t}\, log _e\, \frac{V _{\infty}}{V _{\infty}\, -\, V _t}$

$\displaystyle \frac{1}{15}\, log _e\, \frac{35mL}{(35\, -\, 9)\, mL}\, =\, \frac{1}{15}\, log _e\, \frac{35}{26}$