15. Ideal gases
Avogadro constant (NA)
It is the number of atoms in 0.012 kg of (C-12)
It has the value 6.02 x 1023
Moles (n)
It is the amount of substance containing same number of particles as in 0.012 kg of C-12 or it is the
amount of substance containing a number of particles of that substance equal to the Avogadro
constant NA
Relative Atomic Mass (M)
It is numerically equal to the mass in grams of a mole of atoms. It is also called the molar mass.
Q. Relative Atomic Mass of Mg is 24. Find the number of atoms in 0.12 g of Mg.
Ans. 3.01 x 1021
Unified atomic mass unit (u)
It is defined as (1/12)th of the mass of an atom of C-12.
1u = 1.66 x 10-27 kg (NOT 1.67 x 10-27 kg)
** Mass of an atom in kg = mass number x 1u
Q. Find the mass of one C-12 atom.
Ans. 1.99 x 10-26 kg
** When solving questions with all gas equations, convert Celsius temperatures in to Kelvin.
T / K = T / °C + 273.15
Ideal gas Equation
Ideal gas equation,
n = N/NA, and
Then
Where n = the number of moles
R = the molar gas constant (8.31 J mol-1 K-1)
, Where k = 1.38 × 10–23 J K–1 (the Boltzmann constant)
Definition of an ideal gas
It is a gas which obeys gas laws such as PV = nRT at all pressures, volumes and temperatures in K.
Q1. Nitrogen gas under an initial pressure of 5 x 106 Pa and temperature 15°C is contained in a
cylinder of volume 0.04 m3. After a period of 3 years, the pressure has fallen to 2 x 106 Pa at the same
temperature because of leakage. If the molar mass of nitrogen is 0.028 kg mol-1, calculate
a. Mass of gas originally present in cylinder.
(Ans. 2.34 kg)
b. Mass of gas which escaped from the cylinder in 3 years.
(Ans. 1.4 kg)
c. The average no. of molecules which escaped from the cylinder per second. (Ans. 3.19 x 1017)
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Q2. A cylinder contains 2.40 x 10-3 m3 of gas at 17°C and 2.32 x 106 Pa. Find the number of atoms in
the cylinder.
(Ans. 1.39 x 1024)
Q3. Containers A and B connected by a thin tube with a tap. Initially the connecting tap is closed and
container A has 3m3 gas at 250 K and 5 x 104 Pa. B contains 7.2 m3 of same gas at 400 K and 2 x 104
Pa. Find the pressure after the connecting tap opened, assuming that A is kept at 250 K and B at 400
K.
(Ans, 32000 Pa)
Assumptions about gas molecules related to kinetic theory
a. All molecules behave as identical, hard, perfectly elastic spheres
(They never come to stop and settle at the bottom of the container)
b. They volume of the molecules is negligible when compared with the volume of the container.
(can compress a gas a lot)
c. No forces of attraction or repulsion between molecules.
d. There are many molecules, all moving randomly.
e. The time during a collision is negligible when compared with the time between collisions.
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A Theoritical Model os a Gas
Consider a cube of side L & containing N molecules of gas each of mass m.
Consider the force exerted on the surface X of the cube due to the component speed cx
Change in momentum,
and time between collisions = 2L/ cx
Force =
Pressure = Force/Area, P = F/L2 =
But volume of the cube, L3 = V, Therefore, pressure,
, The mean square of the component speeds in any one of the axes is the same
and therefore,
ρ = Nm/V,
Molecular movement causing pressure:
• Molecules hit and rebound off the walls of the container
• The change in momentum gives rise to force
• Many impulses averaged to give constant force and hence pressure
(Ans.
,
,
,8.9 units)
2. The temperature of a gas is increased in such a way that its volume doubles and its pressure
quadruples. If the rms speed of molecules is 250 ms-1, what is it at the higher temperature?
(Ans. 707 ms-1)
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Relationship between molecular K.E and temperature
KE2/KE1 = T2/T1, ‹C22› / ‹C12› = T2/T1
Gases of higher molecular mass have a smaller rms speeds at constant temperature.
Q1.
(Ans. 1352 ms-1, 478 ms-1)
Q2. He gas occupies a volume of 0.04 m3 at a pressure of 2.0 x 105 Pa and at a temperature of 300 K.
Calculate,
(i) Mass of He,
(ii) RMS speed of its molecules,
(iii) KE of molecules,
(iv) RMS speed at 400 K,
(v) RMS speed of H2 at 300 K. (Assume MHe = 4 g/mol and MH2 = 2 g/mol)
12.8 g, 1367 ms-1, 6.21 x 10-21 J, 1579 ms-1, 1933 ms-1
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