314312
The average velocity and RMS velocity for a group of six particles having speeds 11.2, 9.0, \(\mathrm{8.3,6.5,3.7}\) and \(\mathrm{1.8 \mathrm{~ms}^{-1}}\) are, respectively
Average velocity \(\mathrm{\left(U_{A V}\right)}\) is the of different speeds of all the molecules \(\mathrm{\therefore \quad U_{A V}=\dfrac{11.2+9.0+8.3+6.5+3.7+1.8}{6}}\) \(\mathrm{=\dfrac{40.5}{6}=6.75 \mathrm{~ms}^{-1}}\) Also, \(\mathrm{U_{A V}=0.921 \mathrm{u}}\); where ' \(\mathrm{\mathrm{u}}\) ' is RMS velocity \(\mathrm{\therefore}\) RMS velocity \(\mathrm{\left(U_{\text {rms }}\right)=\dfrac{6.75}{0.9213}=7.47 \mathrm{~ms}^{-1}}\)
CHXI06:STATES OF MATTER
314323
Density ratio of \(\mathrm{O}_{2}\) and \(\mathrm{H}_{2}\) is \(16: 1\). The ratio of their r.m.s. velocities will be
314313
If two gases of molecular weights \(\mathrm{M_{A}}\) and \(\mathrm{M_{B}}\) at temperature \(\mathrm{T_{A}}\) and \(\mathrm{T_{B}, T_{A} M_{B}=T_{B} M_{A}}\), then which property has the same magnitude for both the gases?
1 density
2 Pressure
3 KE per mole
4 \(\mathrm{u_{r m s}}\)
Explanation:
(1) Density of a gas \(\mathrm{(d)=\dfrac{P M}{R T}}\). Since \(\mathrm{\dfrac{M_{B}}{T_{B}}=\dfrac{M_{A}}{T_{A}}}\), at the same pressure \(\mathrm{d_{A}=d_{B}}\). But if pressure is different, then \(\mathrm{d_{A} \neq d_{B}}\). (2) Pressure of the gases would be equal if their densities are equal, otherwise not. (3) KE per mol \(\mathrm{=\dfrac{3}{2} R T}\) Therefore, it will be different for the two gases. (4) \(\mathrm{u_{r m s}=\sqrt{\dfrac{3 R T}{M}}}\), since \(\mathrm{\dfrac{T_{A}}{M_{A}}=\dfrac{T_{B}}{M_{B}} ; u_{r m s}}\) of \(\mathrm{A=u_{r m s}}\) of \(\mathrm{\mathrm{B}}\)
CHXI06:STATES OF MATTER
314314
Which of the following gases has the highest value of rms velocity at \(\mathrm{298 \mathrm{~K}}\) ?
1 \(\mathrm{\mathrm{CH}_{4}}\)
2 \(\mathrm{\mathrm{CO}}\)
3 \(\mathrm{\mathrm{Cl}_{2}}\)
4 \(\mathrm{\mathrm{CO}_{2}}\)
Explanation:
Root mean square velocity, \(\mathrm{U=\sqrt{\dfrac{3 R T}{M}}}\) From the above equation, lower the molecular mass, higher the rms velocity at constant temperature. Molecular weight of \({\rm{C}}{{\rm{H}}_{\rm{4}}}{\rm{ = 16,CO = 28,C}}{{\rm{l}}_{\rm{2}}}{\rm{ = 71,C}}{{\rm{O}}_{\rm{2}}}{\rm{ = 44}}\) So, highest rms velocity shown by \({\rm{C}}{{\rm{H}}_{\rm{4}}}\)
314312
The average velocity and RMS velocity for a group of six particles having speeds 11.2, 9.0, \(\mathrm{8.3,6.5,3.7}\) and \(\mathrm{1.8 \mathrm{~ms}^{-1}}\) are, respectively
Average velocity \(\mathrm{\left(U_{A V}\right)}\) is the of different speeds of all the molecules \(\mathrm{\therefore \quad U_{A V}=\dfrac{11.2+9.0+8.3+6.5+3.7+1.8}{6}}\) \(\mathrm{=\dfrac{40.5}{6}=6.75 \mathrm{~ms}^{-1}}\) Also, \(\mathrm{U_{A V}=0.921 \mathrm{u}}\); where ' \(\mathrm{\mathrm{u}}\) ' is RMS velocity \(\mathrm{\therefore}\) RMS velocity \(\mathrm{\left(U_{\text {rms }}\right)=\dfrac{6.75}{0.9213}=7.47 \mathrm{~ms}^{-1}}\)
CHXI06:STATES OF MATTER
314323
Density ratio of \(\mathrm{O}_{2}\) and \(\mathrm{H}_{2}\) is \(16: 1\). The ratio of their r.m.s. velocities will be
314313
If two gases of molecular weights \(\mathrm{M_{A}}\) and \(\mathrm{M_{B}}\) at temperature \(\mathrm{T_{A}}\) and \(\mathrm{T_{B}, T_{A} M_{B}=T_{B} M_{A}}\), then which property has the same magnitude for both the gases?
1 density
2 Pressure
3 KE per mole
4 \(\mathrm{u_{r m s}}\)
Explanation:
(1) Density of a gas \(\mathrm{(d)=\dfrac{P M}{R T}}\). Since \(\mathrm{\dfrac{M_{B}}{T_{B}}=\dfrac{M_{A}}{T_{A}}}\), at the same pressure \(\mathrm{d_{A}=d_{B}}\). But if pressure is different, then \(\mathrm{d_{A} \neq d_{B}}\). (2) Pressure of the gases would be equal if their densities are equal, otherwise not. (3) KE per mol \(\mathrm{=\dfrac{3}{2} R T}\) Therefore, it will be different for the two gases. (4) \(\mathrm{u_{r m s}=\sqrt{\dfrac{3 R T}{M}}}\), since \(\mathrm{\dfrac{T_{A}}{M_{A}}=\dfrac{T_{B}}{M_{B}} ; u_{r m s}}\) of \(\mathrm{A=u_{r m s}}\) of \(\mathrm{\mathrm{B}}\)
CHXI06:STATES OF MATTER
314314
Which of the following gases has the highest value of rms velocity at \(\mathrm{298 \mathrm{~K}}\) ?
1 \(\mathrm{\mathrm{CH}_{4}}\)
2 \(\mathrm{\mathrm{CO}}\)
3 \(\mathrm{\mathrm{Cl}_{2}}\)
4 \(\mathrm{\mathrm{CO}_{2}}\)
Explanation:
Root mean square velocity, \(\mathrm{U=\sqrt{\dfrac{3 R T}{M}}}\) From the above equation, lower the molecular mass, higher the rms velocity at constant temperature. Molecular weight of \({\rm{C}}{{\rm{H}}_{\rm{4}}}{\rm{ = 16,CO = 28,C}}{{\rm{l}}_{\rm{2}}}{\rm{ = 71,C}}{{\rm{O}}_{\rm{2}}}{\rm{ = 44}}\) So, highest rms velocity shown by \({\rm{C}}{{\rm{H}}_{\rm{4}}}\)
314312
The average velocity and RMS velocity for a group of six particles having speeds 11.2, 9.0, \(\mathrm{8.3,6.5,3.7}\) and \(\mathrm{1.8 \mathrm{~ms}^{-1}}\) are, respectively
Average velocity \(\mathrm{\left(U_{A V}\right)}\) is the of different speeds of all the molecules \(\mathrm{\therefore \quad U_{A V}=\dfrac{11.2+9.0+8.3+6.5+3.7+1.8}{6}}\) \(\mathrm{=\dfrac{40.5}{6}=6.75 \mathrm{~ms}^{-1}}\) Also, \(\mathrm{U_{A V}=0.921 \mathrm{u}}\); where ' \(\mathrm{\mathrm{u}}\) ' is RMS velocity \(\mathrm{\therefore}\) RMS velocity \(\mathrm{\left(U_{\text {rms }}\right)=\dfrac{6.75}{0.9213}=7.47 \mathrm{~ms}^{-1}}\)
CHXI06:STATES OF MATTER
314323
Density ratio of \(\mathrm{O}_{2}\) and \(\mathrm{H}_{2}\) is \(16: 1\). The ratio of their r.m.s. velocities will be
314313
If two gases of molecular weights \(\mathrm{M_{A}}\) and \(\mathrm{M_{B}}\) at temperature \(\mathrm{T_{A}}\) and \(\mathrm{T_{B}, T_{A} M_{B}=T_{B} M_{A}}\), then which property has the same magnitude for both the gases?
1 density
2 Pressure
3 KE per mole
4 \(\mathrm{u_{r m s}}\)
Explanation:
(1) Density of a gas \(\mathrm{(d)=\dfrac{P M}{R T}}\). Since \(\mathrm{\dfrac{M_{B}}{T_{B}}=\dfrac{M_{A}}{T_{A}}}\), at the same pressure \(\mathrm{d_{A}=d_{B}}\). But if pressure is different, then \(\mathrm{d_{A} \neq d_{B}}\). (2) Pressure of the gases would be equal if their densities are equal, otherwise not. (3) KE per mol \(\mathrm{=\dfrac{3}{2} R T}\) Therefore, it will be different for the two gases. (4) \(\mathrm{u_{r m s}=\sqrt{\dfrac{3 R T}{M}}}\), since \(\mathrm{\dfrac{T_{A}}{M_{A}}=\dfrac{T_{B}}{M_{B}} ; u_{r m s}}\) of \(\mathrm{A=u_{r m s}}\) of \(\mathrm{\mathrm{B}}\)
CHXI06:STATES OF MATTER
314314
Which of the following gases has the highest value of rms velocity at \(\mathrm{298 \mathrm{~K}}\) ?
1 \(\mathrm{\mathrm{CH}_{4}}\)
2 \(\mathrm{\mathrm{CO}}\)
3 \(\mathrm{\mathrm{Cl}_{2}}\)
4 \(\mathrm{\mathrm{CO}_{2}}\)
Explanation:
Root mean square velocity, \(\mathrm{U=\sqrt{\dfrac{3 R T}{M}}}\) From the above equation, lower the molecular mass, higher the rms velocity at constant temperature. Molecular weight of \({\rm{C}}{{\rm{H}}_{\rm{4}}}{\rm{ = 16,CO = 28,C}}{{\rm{l}}_{\rm{2}}}{\rm{ = 71,C}}{{\rm{O}}_{\rm{2}}}{\rm{ = 44}}\) So, highest rms velocity shown by \({\rm{C}}{{\rm{H}}_{\rm{4}}}\)
314312
The average velocity and RMS velocity for a group of six particles having speeds 11.2, 9.0, \(\mathrm{8.3,6.5,3.7}\) and \(\mathrm{1.8 \mathrm{~ms}^{-1}}\) are, respectively
Average velocity \(\mathrm{\left(U_{A V}\right)}\) is the of different speeds of all the molecules \(\mathrm{\therefore \quad U_{A V}=\dfrac{11.2+9.0+8.3+6.5+3.7+1.8}{6}}\) \(\mathrm{=\dfrac{40.5}{6}=6.75 \mathrm{~ms}^{-1}}\) Also, \(\mathrm{U_{A V}=0.921 \mathrm{u}}\); where ' \(\mathrm{\mathrm{u}}\) ' is RMS velocity \(\mathrm{\therefore}\) RMS velocity \(\mathrm{\left(U_{\text {rms }}\right)=\dfrac{6.75}{0.9213}=7.47 \mathrm{~ms}^{-1}}\)
CHXI06:STATES OF MATTER
314323
Density ratio of \(\mathrm{O}_{2}\) and \(\mathrm{H}_{2}\) is \(16: 1\). The ratio of their r.m.s. velocities will be
314313
If two gases of molecular weights \(\mathrm{M_{A}}\) and \(\mathrm{M_{B}}\) at temperature \(\mathrm{T_{A}}\) and \(\mathrm{T_{B}, T_{A} M_{B}=T_{B} M_{A}}\), then which property has the same magnitude for both the gases?
1 density
2 Pressure
3 KE per mole
4 \(\mathrm{u_{r m s}}\)
Explanation:
(1) Density of a gas \(\mathrm{(d)=\dfrac{P M}{R T}}\). Since \(\mathrm{\dfrac{M_{B}}{T_{B}}=\dfrac{M_{A}}{T_{A}}}\), at the same pressure \(\mathrm{d_{A}=d_{B}}\). But if pressure is different, then \(\mathrm{d_{A} \neq d_{B}}\). (2) Pressure of the gases would be equal if their densities are equal, otherwise not. (3) KE per mol \(\mathrm{=\dfrac{3}{2} R T}\) Therefore, it will be different for the two gases. (4) \(\mathrm{u_{r m s}=\sqrt{\dfrac{3 R T}{M}}}\), since \(\mathrm{\dfrac{T_{A}}{M_{A}}=\dfrac{T_{B}}{M_{B}} ; u_{r m s}}\) of \(\mathrm{A=u_{r m s}}\) of \(\mathrm{\mathrm{B}}\)
CHXI06:STATES OF MATTER
314314
Which of the following gases has the highest value of rms velocity at \(\mathrm{298 \mathrm{~K}}\) ?
1 \(\mathrm{\mathrm{CH}_{4}}\)
2 \(\mathrm{\mathrm{CO}}\)
3 \(\mathrm{\mathrm{Cl}_{2}}\)
4 \(\mathrm{\mathrm{CO}_{2}}\)
Explanation:
Root mean square velocity, \(\mathrm{U=\sqrt{\dfrac{3 R T}{M}}}\) From the above equation, lower the molecular mass, higher the rms velocity at constant temperature. Molecular weight of \({\rm{C}}{{\rm{H}}_{\rm{4}}}{\rm{ = 16,CO = 28,C}}{{\rm{l}}_{\rm{2}}}{\rm{ = 71,C}}{{\rm{O}}_{\rm{2}}}{\rm{ = 44}}\) So, highest rms velocity shown by \({\rm{C}}{{\rm{H}}_{\rm{4}}}\)
