For gaseous state, if most probable speed is denoted by C ^ * , average speed by ¯ C and root mean square speed by C , then for many molecules, what is the ratios of these speeds?

Correct answer: A. C ^ * : - C : C = 1: 1 .128 : 1 .225 C ^ * = (2RT)/(M) 1 .414:1.595:1.732 - C = (8)/(π)(RT)/(M) C = (3RT)/(M) 2 : (8)/(3.14) : 3 1: 1.128: 1.225 C ^ * : ¯ C : C = 1: 1.128: 1.225

JEE Main 20137 April

Exam: JEE Main
Year: 2013
Date: 7 April
Subject: Chemistry
Chapter: States of Matter

JEE Main 2013 · 7 April · Chemistry · States of Matter

For gaseous state, if most probable speed is denoted by C ^ * ,...

For gaseous state, if most probable speed is denoted by

{C}^{*}

, average speed by

\overset{¯}{C}

and root mean square speed by

C

, then for many molecules, what is the ratios of these speeds?

Options

A ${C}^{*}: \overset{-}{C}: C = 1: 1 .128 : 1 .225$
B ${C}^{*}: \overset{-}{C}: C = 1: 1 .225 : 1 .128$
C ${C}^{*}: \overset{-}{C}: C = 1 .225 : 1 .128 : 1$
D ${C}^{*}: \overset{-}{C}: C = 1 .128 : 1 .225 : 1$

Correct answer

A. ${C}^{*}: \overset{-}{C}: C = 1: 1 .128 : 1 .225$

Step-by-step solution

{C}^{*} = \sqrt{\dfrac{2RT}{M}} 1 .414:1.595:1.732

\overset{-}{C} = \sqrt{\dfrac{8}{\pi}\dfrac{RT}{M}}

C = \sqrt{\dfrac{3RT}{M}}

\sqrt{2} : \sqrt{\dfrac{8}{3.14}} : \sqrt{3}

1: 1.128: 1.225

{C}^{*}: \overset{¯}{C}: C = 1: 1.128: 1.225

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