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1 Kinetic Molecular Model of Gas 1. The kinetic gas equation for 1 mole of a gas 1 mc PV ) 1 1 PV MC ) C 1 mc PV ) PV. At the same temperature and pressure which of the following gas will have highest K.E per mol. H ) O ) CH ) Same for all. The molecular velocities of two gases at the same temperature are U 1 and U their masses are 1 expression is correct? m ) 1U 1 mu 1 U1 m U m and m respectively. Which of the following m ) m1 m ) m1u 1 m U U1 U. The ratio of kinetic energies of equal weights of CH and SO gases under similar conditions is 1 : 1 ) : 1 ) : 1 ) 1 : Hint: KE1:KE=n1:n 5. At what temperature the velocity of SO molecule is same as velocity of O molecule at 7 C 17 C ) 7 C ) 97 C ) 57 C Hint: T1/M1=T/M

2 6. The velocity distribution curve is given below. The correct statement regarding it is As temperature increases the fraction of the molecular having ) T1 T C P increases ) At any temperature C P C ) A small fraction of the molecules have very low velocities 7. SO molecules is times heavier than hydrogen molecules. What will be the ratio of their average kinetic energies at 0K 16 : 1 ) : 1 ) 1 : ) 1 : 1 Hint: K.E of molecule is same for all gases at a given temperature. 8. The average velocity of a gas at 7K is cm / s. What is its r.m.s. velocity at the same temperature cm / s ) cm / s ) cm / s ) cm / s Hint: C = 1.18 C 9. In the kinetic gas equation n represents Number of molecules ) Number of moles ) An integer including zero ) A constant 10. A cubical vessel of side length cm contain 100 molecules with mass of each molecule as 10 7 g. If the r.m.s. velocity of the molecules is 10 cm / s, what is the rate of change of momentum ) dyne / cm ) dyne / cm ) Hint: The rate of change of momentum=mnc dyne / cm dyne / cm T 1 T

3 11. The correct statements regarding max well Boltzmann velocity distribution curve (that is given below) a) T1 T b) As the temperature increases the fraction of the molecules having most probable velocity decreases c) As the temperature increases the value of C increases P d) As the temperature increases r.m.s. velocity of the gas decreases The correct answer is All are correct ) Only a, b and d ) Only b and c ) Only a, b and c 1. The average velocity of a gas is 100 m/s. At the same temperature what is its r.m.s. velocity 11.8 m/s ) 9.1 m/s ) m/s ) m/s Hint: C = 1.18 C 1. R.M.S. velocity of a gas molecule is given by RT M ) KT m ) 8RT M ) PV T 1. At what temperature the r.m.s. velocity of nitrogen gas is twice the most probable velocity of Helium gas at 7 C 57 C ) 5600 C ) 00K ) 600K Hint: C C ofhe RT1 M N N RT M p He 15. The r.m.s. velocity of carbon dioxide gas at 167 C is m/s 500 ) 5000 ) 50 ) 50,000

4 Hint: cm / sec M T 16. What is the increase in K.E. of 10 moles of an ideal gas, when the temperature is increased by 10 C 00 cal ) 00 cal ) 600 cal ) 900 cal Hint: Increase in K.E= (/) nr (dt) litre vessel and litre vessel contained 1 mole each ofo, the temperature are so adjusted such that the velocity of molecules in 1 litre vessel is twice that of litre vessel. At what ratio their pressures will be : 1 ) 8 : 1 ) 6 : ) 1 : At what temperature the rms velocity of oxygen is equal to the most probable velocity of SO at 7 C 100K ) 00K ) 00K ) 9.6K Hint: Refer q.no The K.E. of N molecules of CH is x Joules at 1 C. another sample of CH at 7 C has K.E. of x Joules. The latter sample contains N molecules of CH ) N/ molecules of CH ) N molecules of CH ) N/ molecules of CH Hint: KE1/KE= n1 T1/nT 0. K.E. of one mole of gas is 1.5T Cal ) T Cal ) RT Cal ).5RT Cal Hint: KE= (/) RT 1. The ratio of kinetic energies of equal weights of CH at 100K and SO at 00K is : 1 ) 1 : ) 1 : 1 ) : Hint: KE1/KE= M T1/M1T. The temperature at which ethane molecules have the same average kinetic energy as that of methane molecules at 7 C is

5 7 C ) 7 C ) 97 C ) 67 C Hint: K.E of molecule is same for all gases at a given temperature. R.M.S. velocity of O molecules at 7 C is x cm/sec at what temperature the velocity of O molecules become x cm/sec 600 K ) 7 C ) 97 C ) 17 C C1 T1 Hint: C T. At what temperature the R.M.S. velocity of C H molecules is same as that of N molecules at 00K? 00 C ) 7 C ) 600K ) 97 C Hint: T1 T M M 1 5. At 7 C the ratio of the R.M.S. velocities of ozone and oxygen molecules is ) C1 T1 M Hint:,T1=T C T M 1 6. The R.M.S. velocity of an ideal gas at 0 C is 10 cm/sec. Then its most probable velocity in cm/sec at the same temperature 1180 ) ) ) 1 Hint: Most Probable velocity= X r.m.s. 7. X is an oxide formed in the first excited state of sulphur. Y is a fluoride formed in the second excited state of sulphur. The ratio of average velocities of molecules of X and Y at 5 C and 1 atm is approximately (at. Wts. O = 16, F = 19, S = ) : ) 9 : 10 ) : ) 1 : ) 1 ) 5

6 C1 T1 M Hint:,T1=T C T M 1 8. Boltzmann constant represents the gas constant per One mole of gas )An Avogadro s number of molecules.) Any number of molecules ) One molecule 9. According to kinetic theory, Kinetic Energy = 1 nrt or mv ) nrt or mv 1 ) nrt or mv ) nrt or mv 0 0. Helium atom is two times heavier than a hydrogen molecule at 98 K the average kinetic energy of helium is Two times that of hydrogen molecule ) Same as that of a hydrogen molecule ) Four times that of a hydrogen molecule ) Half that of a hydrogen molecule Hint: K.E of molecule is same for all gases at a given temperature 1. The value of Boltzmann constant is ) ) Joule.K erg.k 6 Joule.K.Molecule.Molecule.Molecule ). 1.8 x 10 J K 1 molecule 1. The ratio between kinetic energies of g of Hydrogen gas and g of Oxygen gas at a given temperature and pressure is : ) : ) 1 : 1 ) 16 : 1 Hint: KE1: KE=n1: n

7 . If the rms velocity of a gas is 1000 metres/sec ; its most probable velocity under similar conditions in metres/sec ) ) Kinetic energy of 10 g of Carbon monoxide gas at 7 C in K.Cals is 1000 ) 1.0 ) 6.0 ).5 ) 9.0 Hint: KE= (/) nrt 5. The ratio of the kinetic energies of equal masses of CH and He at 7 C temperature is 1 : 1 ) 1 : ) : 1 ) : 1 Hint: ke1:ke=m:m1 6. The kinetic energy in K.Cals of 6. gm of O at 7 C is 1.8 K.Cals ) 18 K.Cals ) 180 K.Cals ) 0.18 K.Cals 7. Kinetic theory of gases proves Boyle s law ) Charles s law ) Avogadro s law ) All these laws 8. Which of the following posses greatest amount of Kinetic energy gm of H at 7 C ) gm of O at 0 C ) 16gm of CH at 7 C ) 6gm of O at 0 C Hint: KE is proportional to n x T 9. Which of the following is not the statement of kinetic theory of gases The kinetic energy depends on the temperature of the gas ) The K.E. depends on pressure of the gas ) The collisions are elastic

8 ) Pressure of the gas is due to the collision of the gas molecules with the walls of the vessel 0. At what temperature will the total kinetic energy of 0. mole of He be the same as the total kinetic energy of 0. mole of Ar at 00K 00 K ) 00 K ) 7 K ) 5 K Hint: n1t1= nt KEY ) ) ) 5) 6) 7) 8) 1 9) 1 10) ) 1 16) 17) 18) 1 19) 1 0) ) ) ) 5) 1 6) 7) 1 8) 9) 0) ) ) ) 5) 6) 7) 8) 1 9) 0)