Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
94 views
in Physics by (72.6k points)
closed by

At room temperature (27°C) the rms speed of molecules of a certain diatomic gas is found to be 1930 m/sec. The gas is: 


1. H2
2. F2
3. O2
4. Cl2

1 Answer

0 votes
by (121k points)
selected by
 
Best answer
Correct Answer - Option 1 : H2

Concept:

  • Root Mean Square Speed: It is defined as the square root of the mean of squares of the speed of different molecules.
    • The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.

From the expansion of pressure,

\(P = \frac{1}{3}{\rm{\rho v}}_{rms}^2\)

\({v_{rms}} = \sqrt {\frac{{3P}}{\rho }} \)

\(V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}} \)

\([\because \rho = \frac{M}{V}]\)

⇒ vrms ∝ T 

Where, R = universal gas constant, M = molar mass, P = pressure due to density,ρ = density.

Calculation:

Given that, T = 27°C = 27+273 = 300 K, Vrms = 1930 m/sec

\(V_{rms}= \sqrt {\frac{{3PV}}{{Mass\;of\;gas}}} = \sqrt {\frac{{3RT}}{M}} \)

\(1930 = \sqrt {\frac{{3 \times 8.31 \times {{10}^3} \times 300}}{M}} \)

Mass = 2g, Hence the gas is H2.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...