Advertisements
Advertisements
प्रश्न
Three vessels of equal capacity have gases at the same temperature and pressure. The first vessel contains neon (monatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic).
Is the root mean square speed of molecules the same in the three cases? If not, in which case is vrms the largest?
उत्तर
No. The root mean square speed of neon is the largest.
Since the three vessels have the same capacity, they have the same volume.
Hence, each gas has the same pressure, volume, and temperature.
According to Avogadro’s law, the three vessels will contain an equal number of the respective molecules. This number is equal to Avogadro’s number, N = 6.023 × 1023.
The root mean square speed (vrms) of a gas of mass m, and temperature T, is given by the relation:
`v_"rms" = sqrt((3"kT")/"m")`
Where, k is Boltzmann constant
For the given gases, k and T are constants.
Hence vrms depends only on the mass of the atoms, i.e.,
`V_"rms" prop sqrt(1/"m")`
Therefore, the root mean square speed of the molecules in the three cases is not the same. Among neon, chlorine, and uranium hexafluoride, the mass of neon is the smallest. Hence, neon has the largest root mean square speed among the given gases
APPEARS IN
संबंधित प्रश्न
The figure shows the plot of PV/T versus Pfor 1.00×10–3 kg of oxygen gas at two different temperatures.
(a) What does the dotted plot signify?
(b) Which is true: T1 > T2 or T1 < T2?
(c) What is the value of PV/T where the curves meet on the y-axis?
(d) If we obtained similar plots for 1.00 ×10–3 kg of hydrogen, would we get the same value of PV/T at the point where the curves meet on the y-axis? If not, what mass of hydrogen yields the same value of PV/T (for low pressure high temperature region of the plot)? (Molecular mass of H2 = 2.02 u, of O2 = 32.0 u, R = 8.31 J mo1–1 K–1.)
Estimate the average thermal energy of a helium atom at the temperature of 10 million Kelvin (the typical core temperature in the case of a star).
What do you understand by gas?
Give reasons for the following:
Gas fills the vessel completely in which it is kept.
A gas occupies 500 cm3 at a normal temperature. At what temperature will the volume of the gas be reduced by 20% of its original volume, the pressure is constant?
Estimate the average thermal energy of a helium atom at room temperature (27 °C).
Estimate the average thermal energy of a helium atom at the temperature on the surface of the Sun (6000 K).
Which of the following diagrams (Figure) depicts ideal gas behaviour?
 (a) |
 (b) |
 (c) |
 (d) |
Calculate the number of atoms in 39.4 g gold. Molar mass of gold is 197g mole–1.
Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will ______.
