Molecular Speeds and Maxwell – Boltzmann Distribution Curves
CHXI06:STATES OF MATTER

314315 What is the temperature at which oxygen molecules have the same r.m.s. velocity as the hydrogen molecules at \(\mathrm{27^{\circ} \mathrm{C}}\) ?

1 \(\mathrm{3527^{\circ} \mathrm{C}}\)
2 \(\mathrm{4227^{\circ} \mathrm{C}}\)
3 \(\mathrm{4527^{\circ} \mathrm{C}}\)
4 \(\mathrm{4000^{\circ} \mathrm{C}}\)
CHXI06:STATES OF MATTER

314316 Match the Column I with Column II and choose the correct option
Column I
Column II
A
\(\mathrm{u_{a v}}\)
P
\(\mathrm{\sqrt{\dfrac{3 R T}{M}}}\)
B
\(\mathrm{u_{r m s}}\)
Q
\(\mathrm{\sqrt{\dfrac{8 R T}{\pi M}}}\)
C
\(\mathrm{u_{m p}}\)
R
\(\mathrm{\sqrt{\dfrac{2 R T}{\pi M}}}\)
S
\(\mathrm{\sqrt{\dfrac{2 R T}{M}}}\)

1 A - Q, B - P, C - S
2 A - P, B - Q, C - R
3 A - R, B - P, C - Q
4 A - S, B - P, C - Q
CHXI06:STATES OF MATTER

314317 For gaseous state, if most probable speed is denoted by \(\mathrm{C^{*}}\), average speed by \(\mathrm{\bar{C}}\) means square speed by \(\mathrm{\mathrm{C}}\), then for a large number of molecules, the ratios of these speeds are

1 \(\mathrm{C^{*}: \bar{C}: C=1.225: 1.128: 1}\)
2 \(\mathrm{C^{*}: \bar{C}: C=1.128: 1.225: 1}\)
3 \(\mathrm{C^{*}: \bar{C}: C=1: 1.128: 1.225}\)
4 \(\mathrm{C^{*}: \bar{C}: C=1: 1.225: 1.128}\)
CHXI06:STATES OF MATTER

314318 The average velocity (in \(\mathrm{cm} / \mathrm{s}\) ) of hydrogen molecule at \(27^{\circ} \mathrm{C}\) will be

1 \(19.3 \times 10^{4}\)
2 \(17.8 \times 10^{4}\)
3 \(24.93 \times 10^{9}\)
4 \(17.8 \times 10^{8}\)
CHXI06:STATES OF MATTER

314319 For one mole of hydrogen gas, kinetic energy is \(\mathrm{4 \times 10^{8}}\) ergs. Then its RMS velocity is

1 \(\mathrm{4 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
2 \(\mathrm{2 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
3 \(\mathrm{10^{7} / 4 \mathrm{~cm} / \mathrm{sec}}\)
4 \(\mathrm{10^{4} \mathrm{~cm} / \mathrm{sec}}\)
CHXI06:STATES OF MATTER

314315 What is the temperature at which oxygen molecules have the same r.m.s. velocity as the hydrogen molecules at \(\mathrm{27^{\circ} \mathrm{C}}\) ?

1 \(\mathrm{3527^{\circ} \mathrm{C}}\)
2 \(\mathrm{4227^{\circ} \mathrm{C}}\)
3 \(\mathrm{4527^{\circ} \mathrm{C}}\)
4 \(\mathrm{4000^{\circ} \mathrm{C}}\)
CHXI06:STATES OF MATTER

314316 Match the Column I with Column II and choose the correct option
Column I
Column II
A
\(\mathrm{u_{a v}}\)
P
\(\mathrm{\sqrt{\dfrac{3 R T}{M}}}\)
B
\(\mathrm{u_{r m s}}\)
Q
\(\mathrm{\sqrt{\dfrac{8 R T}{\pi M}}}\)
C
\(\mathrm{u_{m p}}\)
R
\(\mathrm{\sqrt{\dfrac{2 R T}{\pi M}}}\)
S
\(\mathrm{\sqrt{\dfrac{2 R T}{M}}}\)

1 A - Q, B - P, C - S
2 A - P, B - Q, C - R
3 A - R, B - P, C - Q
4 A - S, B - P, C - Q
CHXI06:STATES OF MATTER

314317 For gaseous state, if most probable speed is denoted by \(\mathrm{C^{*}}\), average speed by \(\mathrm{\bar{C}}\) means square speed by \(\mathrm{\mathrm{C}}\), then for a large number of molecules, the ratios of these speeds are

1 \(\mathrm{C^{*}: \bar{C}: C=1.225: 1.128: 1}\)
2 \(\mathrm{C^{*}: \bar{C}: C=1.128: 1.225: 1}\)
3 \(\mathrm{C^{*}: \bar{C}: C=1: 1.128: 1.225}\)
4 \(\mathrm{C^{*}: \bar{C}: C=1: 1.225: 1.128}\)
CHXI06:STATES OF MATTER

314318 The average velocity (in \(\mathrm{cm} / \mathrm{s}\) ) of hydrogen molecule at \(27^{\circ} \mathrm{C}\) will be

1 \(19.3 \times 10^{4}\)
2 \(17.8 \times 10^{4}\)
3 \(24.93 \times 10^{9}\)
4 \(17.8 \times 10^{8}\)
CHXI06:STATES OF MATTER

314319 For one mole of hydrogen gas, kinetic energy is \(\mathrm{4 \times 10^{8}}\) ergs. Then its RMS velocity is

1 \(\mathrm{4 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
2 \(\mathrm{2 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
3 \(\mathrm{10^{7} / 4 \mathrm{~cm} / \mathrm{sec}}\)
4 \(\mathrm{10^{4} \mathrm{~cm} / \mathrm{sec}}\)
CHXI06:STATES OF MATTER

314315 What is the temperature at which oxygen molecules have the same r.m.s. velocity as the hydrogen molecules at \(\mathrm{27^{\circ} \mathrm{C}}\) ?

1 \(\mathrm{3527^{\circ} \mathrm{C}}\)
2 \(\mathrm{4227^{\circ} \mathrm{C}}\)
3 \(\mathrm{4527^{\circ} \mathrm{C}}\)
4 \(\mathrm{4000^{\circ} \mathrm{C}}\)
CHXI06:STATES OF MATTER

314316 Match the Column I with Column II and choose the correct option
Column I
Column II
A
\(\mathrm{u_{a v}}\)
P
\(\mathrm{\sqrt{\dfrac{3 R T}{M}}}\)
B
\(\mathrm{u_{r m s}}\)
Q
\(\mathrm{\sqrt{\dfrac{8 R T}{\pi M}}}\)
C
\(\mathrm{u_{m p}}\)
R
\(\mathrm{\sqrt{\dfrac{2 R T}{\pi M}}}\)
S
\(\mathrm{\sqrt{\dfrac{2 R T}{M}}}\)

1 A - Q, B - P, C - S
2 A - P, B - Q, C - R
3 A - R, B - P, C - Q
4 A - S, B - P, C - Q
CHXI06:STATES OF MATTER

314317 For gaseous state, if most probable speed is denoted by \(\mathrm{C^{*}}\), average speed by \(\mathrm{\bar{C}}\) means square speed by \(\mathrm{\mathrm{C}}\), then for a large number of molecules, the ratios of these speeds are

1 \(\mathrm{C^{*}: \bar{C}: C=1.225: 1.128: 1}\)
2 \(\mathrm{C^{*}: \bar{C}: C=1.128: 1.225: 1}\)
3 \(\mathrm{C^{*}: \bar{C}: C=1: 1.128: 1.225}\)
4 \(\mathrm{C^{*}: \bar{C}: C=1: 1.225: 1.128}\)
CHXI06:STATES OF MATTER

314318 The average velocity (in \(\mathrm{cm} / \mathrm{s}\) ) of hydrogen molecule at \(27^{\circ} \mathrm{C}\) will be

1 \(19.3 \times 10^{4}\)
2 \(17.8 \times 10^{4}\)
3 \(24.93 \times 10^{9}\)
4 \(17.8 \times 10^{8}\)
CHXI06:STATES OF MATTER

314319 For one mole of hydrogen gas, kinetic energy is \(\mathrm{4 \times 10^{8}}\) ergs. Then its RMS velocity is

1 \(\mathrm{4 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
2 \(\mathrm{2 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
3 \(\mathrm{10^{7} / 4 \mathrm{~cm} / \mathrm{sec}}\)
4 \(\mathrm{10^{4} \mathrm{~cm} / \mathrm{sec}}\)
CHXI06:STATES OF MATTER

314315 What is the temperature at which oxygen molecules have the same r.m.s. velocity as the hydrogen molecules at \(\mathrm{27^{\circ} \mathrm{C}}\) ?

1 \(\mathrm{3527^{\circ} \mathrm{C}}\)
2 \(\mathrm{4227^{\circ} \mathrm{C}}\)
3 \(\mathrm{4527^{\circ} \mathrm{C}}\)
4 \(\mathrm{4000^{\circ} \mathrm{C}}\)
CHXI06:STATES OF MATTER

314316 Match the Column I with Column II and choose the correct option
Column I
Column II
A
\(\mathrm{u_{a v}}\)
P
\(\mathrm{\sqrt{\dfrac{3 R T}{M}}}\)
B
\(\mathrm{u_{r m s}}\)
Q
\(\mathrm{\sqrt{\dfrac{8 R T}{\pi M}}}\)
C
\(\mathrm{u_{m p}}\)
R
\(\mathrm{\sqrt{\dfrac{2 R T}{\pi M}}}\)
S
\(\mathrm{\sqrt{\dfrac{2 R T}{M}}}\)

1 A - Q, B - P, C - S
2 A - P, B - Q, C - R
3 A - R, B - P, C - Q
4 A - S, B - P, C - Q
CHXI06:STATES OF MATTER

314317 For gaseous state, if most probable speed is denoted by \(\mathrm{C^{*}}\), average speed by \(\mathrm{\bar{C}}\) means square speed by \(\mathrm{\mathrm{C}}\), then for a large number of molecules, the ratios of these speeds are

1 \(\mathrm{C^{*}: \bar{C}: C=1.225: 1.128: 1}\)
2 \(\mathrm{C^{*}: \bar{C}: C=1.128: 1.225: 1}\)
3 \(\mathrm{C^{*}: \bar{C}: C=1: 1.128: 1.225}\)
4 \(\mathrm{C^{*}: \bar{C}: C=1: 1.225: 1.128}\)
CHXI06:STATES OF MATTER

314318 The average velocity (in \(\mathrm{cm} / \mathrm{s}\) ) of hydrogen molecule at \(27^{\circ} \mathrm{C}\) will be

1 \(19.3 \times 10^{4}\)
2 \(17.8 \times 10^{4}\)
3 \(24.93 \times 10^{9}\)
4 \(17.8 \times 10^{8}\)
CHXI06:STATES OF MATTER

314319 For one mole of hydrogen gas, kinetic energy is \(\mathrm{4 \times 10^{8}}\) ergs. Then its RMS velocity is

1 \(\mathrm{4 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
2 \(\mathrm{2 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
3 \(\mathrm{10^{7} / 4 \mathrm{~cm} / \mathrm{sec}}\)
4 \(\mathrm{10^{4} \mathrm{~cm} / \mathrm{sec}}\)
CHXI06:STATES OF MATTER

314315 What is the temperature at which oxygen molecules have the same r.m.s. velocity as the hydrogen molecules at \(\mathrm{27^{\circ} \mathrm{C}}\) ?

1 \(\mathrm{3527^{\circ} \mathrm{C}}\)
2 \(\mathrm{4227^{\circ} \mathrm{C}}\)
3 \(\mathrm{4527^{\circ} \mathrm{C}}\)
4 \(\mathrm{4000^{\circ} \mathrm{C}}\)
CHXI06:STATES OF MATTER

314316 Match the Column I with Column II and choose the correct option
Column I
Column II
A
\(\mathrm{u_{a v}}\)
P
\(\mathrm{\sqrt{\dfrac{3 R T}{M}}}\)
B
\(\mathrm{u_{r m s}}\)
Q
\(\mathrm{\sqrt{\dfrac{8 R T}{\pi M}}}\)
C
\(\mathrm{u_{m p}}\)
R
\(\mathrm{\sqrt{\dfrac{2 R T}{\pi M}}}\)
S
\(\mathrm{\sqrt{\dfrac{2 R T}{M}}}\)

1 A - Q, B - P, C - S
2 A - P, B - Q, C - R
3 A - R, B - P, C - Q
4 A - S, B - P, C - Q
CHXI06:STATES OF MATTER

314317 For gaseous state, if most probable speed is denoted by \(\mathrm{C^{*}}\), average speed by \(\mathrm{\bar{C}}\) means square speed by \(\mathrm{\mathrm{C}}\), then for a large number of molecules, the ratios of these speeds are

1 \(\mathrm{C^{*}: \bar{C}: C=1.225: 1.128: 1}\)
2 \(\mathrm{C^{*}: \bar{C}: C=1.128: 1.225: 1}\)
3 \(\mathrm{C^{*}: \bar{C}: C=1: 1.128: 1.225}\)
4 \(\mathrm{C^{*}: \bar{C}: C=1: 1.225: 1.128}\)
CHXI06:STATES OF MATTER

314318 The average velocity (in \(\mathrm{cm} / \mathrm{s}\) ) of hydrogen molecule at \(27^{\circ} \mathrm{C}\) will be

1 \(19.3 \times 10^{4}\)
2 \(17.8 \times 10^{4}\)
3 \(24.93 \times 10^{9}\)
4 \(17.8 \times 10^{8}\)
CHXI06:STATES OF MATTER

314319 For one mole of hydrogen gas, kinetic energy is \(\mathrm{4 \times 10^{8}}\) ergs. Then its RMS velocity is

1 \(\mathrm{4 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
2 \(\mathrm{2 \times 10^{4} \mathrm{~cm} / \mathrm{sec}}\)
3 \(\mathrm{10^{7} / 4 \mathrm{~cm} / \mathrm{sec}}\)
4 \(\mathrm{10^{4} \mathrm{~cm} / \mathrm{sec}}\)