MyQuestionIcon

1

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

Molecular Speeds - Vrms, Vavg, Vmps

Two chamber c...

Question

Two chamber containing $m_{1}$ and $m_{2}$ grams of a gas at pressure $P_{1}$ and $P_{2}$ respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be.

A

\frac{P_{1} P_{2} (m_{1} + m_{2})}{P_{2} m_{1} + P_{1} m_{2}}

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

B

\frac{P_{1} P_{2} m_{1}}{P_{2} m_{1} + P_{1} m_{2}}

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

C

\frac{m_{1} m_{2} (P_{1} + P_{2})}{P_{2} m_{1} + P_{1} m_{2}}

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

D

\frac{m_{1} m_{2} P_{2}}{P_{2} m_{1} + P_{1} m_{2}}

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

Open in App

Solution

The correct option is C $\frac{P_{1} P_{2} (m_{1} + m_{2})}{P_{2} m_{1} + P_{1} m_{2}}$
According to Boyle's law, PV $=$ kT(a constant)
or $P \frac{m}{ρ} =$ kT or $ρ = \frac{P m}{k T}$

or $ρ = \frac{P}{K}$ (where $\frac{k T}{m} = K$ a constant)

So, $ρ_{1} = \frac{P_{1}}{K}$ and $V_{1} = \frac{m_{1}}{ρ_{1}} = \frac{m_{1}}{P_{1} / K} = \frac{K m_{1}}{P_{1}}$
Similarly, $V_{2} = \frac{K m_{2}}{P_{2}}$
Total volume $= V_{1} + V_{2} = K (\frac{m_{1}}{P_{1}} + \frac{m_{2}}{P_{2}})$

Let P be the common pressure and $ρ$ be the common density of mixture. Then.
$ρ = \frac{m_{1} + m_{2}}{V_{1} + V_{2}} = \frac{m_{1} + m_{2}}{K (\frac{m_{1}}{P_{1}} + \frac{m_{2}}{P_{2}})}$

$∴ P = K_{ρ} = \frac{m_{1} + m_{2}}{\frac{m_{1}}{P_{1}} + \frac{m_{2}}{P_{2}}} = \frac{P_{1} P_{2} (m_{1} + m_{2})}{(m_{1} P_{2} + m_{2} P_{1})}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Two chambers containing

m_{1}

m_{2}

gm of a gas at pressure

P_{1}

P_{2}

respectively are put in communication with each other, temperature remaining constant. The common pressure reached will be

Q. Two chambers, one containing

m_{1}

P_{1}

pressure and other containing

m_{2}

P_{2}

pressure, are put in communication with each other. If temperature remains constant, the common pressure reached will be:

Q. Two chambers, one containing

m_{1} g

P_{1}

pressure and other containing

m_{2} g

P_{2}

pressure are put in communication with each other. If temperature remains constant, the common pressure reached will be:

Two containers of equal volume contain the same gas at pressures $P_{1}$ and $P_{2}$ and absolute temperatures $T_{1}$ and $T_{2}$ respectively. On joining the vessels, the gas reaches a common pressure P and common temperature T. The ratio $\frac{P}{T}$ is equal to

Q. Two containers of equal volume contain the same gas at pressures

P_{1}

P_{2}

and absolute temperatures

T_{1}

T_{2}

, respectively. On joining the vessels, the gas reaches a common pressure

P

and common temperature

T

\frac{P}{T}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

CHEMISTRY

Watch in App

explore_more_icon

Explore more

Molecular Speeds - Vrms, Vavg, Vmps

Standard XII Chemistry

Join BYJU'S Learning Program

CrossIcon