Question:
What is the mass of $ 2\,L $ of nitrogen at $ 22.4\,arm $ pressure and $ 273\,K $ ?
What is the mass of $ 2\,L $ of nitrogen at $ 22.4\,arm $ pressure and $ 273\,K $ ?
Updated On: Jun 6, 2024
- $ 28\,g $
- $ 14\times 22.4\,g $
- $ 56\,g $
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
From ideal gas equation
$pV = nRT $
where $p$ is pressure,
$V$ the volume,
$R$ the gas constant,
$T$ the temperature and
$n$ the number of moles.
$\therefore n=\frac{p V}{R T}$
Given $ p =22.4\, atm$ pressure
$=22.4 \times 1.01 \times 10^{5} Nm ^{-2}$
$V=2 L=2 \times 10^{-3} m ^{3}$
$ R=8.31 \,J\,mol ^{-1}- K ^{-1}$
$ T =273 \,K$
$\therefore n=\frac{22.4 \times 1.01 \times 10^{5} \times 2 \times 10^{-3}}{8.31 \times 273}$
$ n=1.99 \approx 2$
$\therefore n=\frac{\text { mass }}{\text { atomic weigh }}$
We have mass $=n \times$ atomic weight
$=2 \times 14=28 \,g$
$pV = nRT $
where $p$ is pressure,
$V$ the volume,
$R$ the gas constant,
$T$ the temperature and
$n$ the number of moles.
$\therefore n=\frac{p V}{R T}$
Given $ p =22.4\, atm$ pressure
$=22.4 \times 1.01 \times 10^{5} Nm ^{-2}$
$V=2 L=2 \times 10^{-3} m ^{3}$
$ R=8.31 \,J\,mol ^{-1}- K ^{-1}$
$ T =273 \,K$
$\therefore n=\frac{22.4 \times 1.01 \times 10^{5} \times 2 \times 10^{-3}}{8.31 \times 273}$
$ n=1.99 \approx 2$
$\therefore n=\frac{\text { mass }}{\text { atomic weigh }}$
We have mass $=n \times$ atomic weight
$=2 \times 14=28 \,g$
Was this answer helpful?
0
0
Top Questions on kinetic theory
- When a system of multiple long narrow slits (width 2µm and period 4µm) is illuminated with a laser of wavelength 600nm. There are 40 minima between the two consecutive principal maxima observed in its diffraction pattern. Then maximum resolving power of the system is _______
- IIT JAM - 2024
- Physics
- kinetic theory
- A cylinder-piston system contains N atoms of an ideal gas. If 𝑡𝑎𝑣𝑔 is the average time between successive collisions of a given atom with other atoms. If the temperature T of the gas is increased isobarically, then 𝑡𝑎𝑣𝑔 is proportional to :
- IIT JAM - 2024
- Physics
- kinetic theory
- A one-dimensional infinite square-well potential is given by:
\(v(x)=0\,\,for\,\,-\frac{a}{2}<x<+\frac{a}{2}\)= ∞ elsewhere
Let 𝐸𝑒 (𝑥) and ψ𝑒 (𝑥) be the ground state energy and the corresponding wave function, respectively, if an electron (e) is trapped in that well. Similarly, let 𝐸µ(𝑥) and ψµ (𝑥) be the corresponding quantities, if a muon (µ) is trapped in the well. Choose the correct option:- IIT JAM - 2024
- Physics
- kinetic theory
- A gas consists of particles, each having three translational and three rotational degrees of freedom. The ratio of specific heats, Cp/Cv, is: (Cp and Cv are the specific heats at constant pressure and constant volume, respectively).
- IIT JAM - 2024
- Physics
- kinetic theory
- A stationary nitrogen (\(^{14}_7N\)) nucleus is bombarded with α- particle (\(^{4}_2He\)) and the following nuclear reaction takes place:
If the kinetic energies of \(^4_2\) and \(^4_2H\) are 5.314MeV and 4.012MeV, respectively, then the kinetic energy of \(^{17}_80\) is MeV. (Rounded off to one decimal place)
(Masses are given in units of 𝑢 = 931.5MeV/c2 )- IIT JAM - 2024
- Physics
- kinetic theory
View More Questions
Questions Asked in JKCET exam
- A moving block having mass $m$, collides with another stationary block having mass $4\,m$. The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of coefficient of restitution (e) will be
- JKCET - 2019
- work, energy and power
- A force $ F = 3x^2 + 2x + 1 $ acts on a body in the $ x $ -direction. The work done by this force during a displacement from $ x = -1 $ to $ +1 $ is
- JKCET - 2019
- work, energy and power
- What is the colour of the flame on heating potassium in the flame of a Bunsen burner?
- JKCET - 2019
- GROUP 1 ELEMENTS
- If $ a $ , $ b $ , $ c $ are the lengths of three edges of unit cell, $ \alpha $ is the angle between side $ b $ and $ c $ , $ \beta $ is the angle between side $ a $ and $ c $ and $ \gamma $ is the angle between side $ a $ and $ b $ , what is the Bravais Lattice dimensions of a tetragonal crystal?
- JKCET - 2019
- The solid state
- Which of the following compounds is known as copper glance?
- JKCET - 2019
- General Principles and Processes of Isolation of Elements
View More Questions
Concepts Used:
Kinetic Molecular Theory of Gases
Postulates of Kinetic Theory of Gases:
- Gases consist of particles in constant, random motion. They continue in a straight line until they collide with each other or the walls of their container.
- Particles are point masses with no volume. The particles are so small compared to the space between them, that we do not consider their size in ideal gases.
- Gas pressure is due to the molecules colliding with the walls of the container. All of these collisions are perfectly elastic, meaning that there is no change in energy of either the particles or the wall upon collision. No energy is lost or gained from collisions. The time it takes to collide is negligible compared with the time between collisions.
- The kinetic energy of a gas is a measure of its Kelvin temperature. Individual gas molecules have different speeds, but the temperature and
kinetic energy of the gas refer to the average of these speeds. - The average kinetic energy of a gas particle is directly proportional to the temperature. An increase in temperature increases the speed in which the gas molecules move.
- All gases at a given temperature have the same average kinetic energy.
- Lighter gas molecules move faster than heavier molecules.
