Question:
The molecules of which of the following gases has the highest speed?
The molecules of which of the following gases has the highest speed?
Updated On: May 17, 2022
\({O_2}\) at \(0^{\circ} C\)
\({N_2}\) at \(1000^{\circ} C\)
\({CH_4}\) at 298K
\({H_2}\) at \( - 50^{\circ} C\)
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The Correct Option is D
Solution and Explanation
(a) Velocity of particle $\left(v_{rms}\right)=\sqrt{\frac{3RT}{M}}$
$O_{2}$ at $0^{\circ}C=\sqrt{\frac{3\times R\times273}{32}}=\sqrt{25.5R}$
(b) $N_2$ at $1000^{\circ}C$
$=\sqrt{\frac{3\times R\times1273}{28}}=\sqrt{136.3R}$
(c) $CH_4$ at $298\,K=\sqrt{\frac{3\times R\times298}{16}}=\sqrt{55.8R}$
(d) $H_2$ at $-50^{\circ}C$
$=\sqrt{\frac{3\times R\times223}{2}}$
$=\sqrt{334.5R}$
Hence, $H_2$ has the highest speed.
$O_{2}$ at $0^{\circ}C=\sqrt{\frac{3\times R\times273}{32}}=\sqrt{25.5R}$
(b) $N_2$ at $1000^{\circ}C$
$=\sqrt{\frac{3\times R\times1273}{28}}=\sqrt{136.3R}$
(c) $CH_4$ at $298\,K=\sqrt{\frac{3\times R\times298}{16}}=\sqrt{55.8R}$
(d) $H_2$ at $-50^{\circ}C$
$=\sqrt{\frac{3\times R\times223}{2}}$
$=\sqrt{334.5R}$
Hence, $H_2$ has the highest speed.
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Concepts Used:
Gas Laws
The gas laws were developed at the end of the 18th century, when scientists began to realize that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases.
The five gas laws are:
- Boyle’s Law, which provides a relationship between the pressure and the volume of a gas.
- Charles’s Law, which provides a relationship between the volume occupied by a gas and the absolute temperature.
- Gay-Lussac’s Law, which provides a relationship between the pressure exerted by a gas on the walls of its container and the absolute temperature associated with the gas.
- Avogadro’s Law, which provides a relationship between the volume occupied by a gas and the amount of gaseous substance.
- The Combined Gas Law (or the Ideal Gas Law), which can be obtained by combining the four laws listed above.