Advertisements
Advertisements
Question
Calculate the average molecular kinetic energy
- per kmol
- per kg
- per molecule
of oxygen at 127°C, given that the molecular weight of oxygen is 32, R is 8.31 J mol−1K−1 and Avogadro’s number NA is 6.02 × 1023 molecules mol−1.
Advertisements
Solution
Data: T = 273 + 127 = 400 K,
molecular weight = 32
∴ molar mass = 32 kg/kmol,
R = 8.31 Jmol-1K-1,
NA = 6.02 × 1023 molecules mol-1
(i) The average molecular kinetic energy per kmol of oxygen = the average kinetic energy per mol of oxygen × 1000
`= 3/2 "RT" xx 1000`
= `3/2(8.31)(400)(10^3)"J"/"kmol"`
= (600)(8.31)(103)
= 4.986 × 106 J/kmol
(ii) The average molecular kinetic energy per kg of oxygen
= `3/2 "RT"/"M"_0`
= `(4.986xx10^6 "J"//"mol")/(32 "kg"//"kmol")`
= 1.558 × 105 J/kg.
(iii) The average molecular kinetic energy per molecule of oxygen
= `3/2 "RT"/"N"_"A"`
= `(4.986 xx 10^6 "J"//"mol")/(6.02 xx 10^23 "molecule"//"mol")`
= 8.282 × 10-21 J/molecule
APPEARS IN
RELATED QUESTIONS
Do you expect the gas in a cooking gas cylinder to obey the ideal gas equation?
Which of the following parameters is the same for molecules of all gases at a given temperature?
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
The process on an ideal gas, shown in figure, is
Which of the following quantities is the same for all ideal gases at the same temperature?
(a) The kinetic energy of 1 mole
(b) The kinetic energy of 1 g
(c) The number of molecules in 1 mole
(d) The number of molecules in 1 g
Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m3. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m3. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.
Use R = 8.3 J K-1 mol-1
0.040 g of He is kept in a closed container initially at 100.0°C. The container is now heated. Neglecting the expansion of the container, calculate the temperature at which the internal energy is increased by 12 J.
Use R = 8.3 J K-1 mol-1
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg in figure. The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
Using figure, find the boiling point of methyl alcohol at 1 atm (760 mm of mercury) and at 0.5 atm.
Answer in brief:
A gas in a cylinder is at pressure P. If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then find the resultant pressure.
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively).
In an ideal gas, the molecules possess ______.
Explain, on the basis of the kinetic theory of gases, how the pressure of a gas changes if its volume is reduced at a constant temperature.
The power radiated by a perfect blackbody depends only on its ______
Calculate the energy radiated in one minute by a blackbody of surface area 200 cm2 at 127 °C (σ = 5.7 x 10-8 J m-2 s-1 K-4)
On what, the values of absorption coefficient, reflection coefficient, and transmission coefficient depend, in addition to the material of the object on which the radiation is an incident?
Why the temperature of all bodies remains constant at room temperature?
Above what temperature, all bodies radiate electromagnetic radiation?
If the density of nitrogen is 1.25 kg/m3 at a pressure of 105 Pa, find the root mean square velocity of nitrogen molecules.
Compare the rate of radiation of metal bodies at 727 °C and 227 °C.
A metal cube of length 4 cm radiates heat at the rate of 10 J/s. Find its emissive power at a given temperature.
The average translational kinetic energy of a molecule in a gas is 'E1'. The kinetic energy of the electron (e) accelerated from rest through p.d. 'V' volt is 'E2'. The temperature at which E1 = E2 is possible, is ______.
Volume versus temperature graphs for a given mass of an ideal gas are shown in figure at two different values of constant pressure. What can be inferred about relation between P1 and P2?
An insulated container containing monoatomic gas of molar mass m is moving with a velocity vo. If the container is suddenly stopped, find the change in temperature.
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, KP are related as ______.
For a particle moving in vertical circle, the total energy at different positions along the path ______.
Two gases A and B are at absolute temperatures of 360 K and 420 K, respectively. The ratio of the average kinetic energy of the molecules of gas B to that of gas A is ______.
Assuming the expression for the pressure P exerted by an ideal gas, prove that the kinetic energy per unit volume of the gas is `3/2` P.
If a = 0. 72 and t = 0.04, then the value of r is ______.
