MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

First Order Reaction

For a first o...

Question

For a first order reaction, $A (g) \to 2 B (g) + C (g)$ , the rate constant in terms of initial pressure $P_{0}$ and pressure at time $t (P_{t})$ , is given by:

A

\frac{1}{t} l n \frac{P_{0}}{P_{t} - P_{0}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

\frac{1}{t} l n \frac{2 P_{0}}{3 P_{0} - P_{t}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

\frac{1}{t} l n \frac{3 P_{0}}{P_{t} - P_{0}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{1}{t} l n \frac{3 P_{0}}{3 P_{t} - P_{0}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{1}{t} l n \frac{2 P_{0}}{3 P_{0} - P_{t}}$
$A (g) \to 2 B (g) + C (g)$
$Initial pressure P_{0} 00$
$Pressure after time t (P_{0} - P) 2 P P$
Total pressure of the reaction mixture after time t,
$P_{t} = (P_{0} - P) + 2 P + P$
$\Rightarrow P_{t} = P_{0} + 2 P$
$\Rightarrow P = \frac{P_{t} - P_{0}}{2}$
Pressure of A after time $t (P_{A}) = P_{0} - P$
$\Rightarrow P_{A} = P_{0} - \frac{(P_{t} - P_{0})}{2}$
$\Rightarrow P_{A} = \frac{2 P_{0} - (P_{t} - P_{0})}{2}$
$\Rightarrow P_{A} = \frac{3 P_{0} - P_{t}}{2}$
$But initial pressure of A (P_{0}) \propto initial concentration of A, i . e . [A_{0}]$
$Pressure of A after time t (P_{A}) \propto concentration of A at time t is [A]$
Substituting these values in the first order rate equation,
$K = \frac{1}{t} l n \frac{[A_{0}]}{[A]}$
We get,
$K = \frac{1}{t} l n \frac{P_{0}}{\frac{3 P_{0} - P_{t}}{2}}$
$\Rightarrow K = \frac{1}{t} l n \frac{2 P_{0}}{3 P_{0} - P_{t}}$

Suggest Corrections

thumbs-up

20

Similar questions

Q. For first order homogeneous gaseous reaction A → 2B + C, the initial pressure was

P_{0}

while total pressure at time 't' was

P_{t}

. The expression for the rate constant

k

P_{0}, P_{t}

Q. For the first order homogeneous gaseous reaction

A \to 2 B + C

, the initial pressure was

P_{i}

while total pressure at time 't' was

P_{t}

. Write expression for the rate constant k in terms of

P_{i}, P_{t}

t

.

Q. For a first order gas phase reaction:

A_{(g)} \to 2 B_{(g)} + C_{(g)}

P_{0}

be initial pressure of

A

P

, the total pressure at time '

t^{'}

. Integrated rate equation is:

For a first order reaction $A (g) \to 2 B (g) + C (g)$ at constant volume and 300 K, the total pressure at the beginning (t=0) and time t are $P_{o}$ and $P_{t}$ respectively. Initially, only $A$ is present with concentration $[A]_{o}$ and $t_{1 / 2}$ is the time required for the partial pressure of $A$ to reach a third of its initial value. The correct options are:
(Assume that all these gases behave as ideal gaes)

Q. Consider a first order gas phase decomposition reaction given below:

A_{(g)} \to B_{(g)} + C_{(g)}

The initial pressure of the system before decomposition of

A

p_{i}

. After a lapse of time

^{'} t^{'}

total pressure of the system increased by

x

units and became

^{'} p_{t}^{'}

.
The rate constant

k

for the reaction is given as:

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Integrated Rate Equations

CHEMISTRY

Watch in App

explore_more_icon

Explore more

First Order Reaction

Standard XII Chemistry

Join BYJU'S Learning Program

CrossIcon