RMS speed of gas molecules: Class 11 practice
v_rms = √(3RT/M) with M in kg/mol and T in kelvin. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Square roots
The idea behind rms speed of gas molecules
v_rms = √(3RT/M) with M in kg/mol and T in kelvin. Average kinetic energy per molecule = (3/2)kT. Doubling absolute temperature raises v_rms by √2.
Step-by-step method
- Convert M to kg/mol and T to K.
- v_rms = √(3RT/M).
- For ratios use v ∝ √(T/M).
Worked example 1 (Basic)
Find the rms speed of N₂ molecules at 461 K.
- v = √(3 × 8.314 × 461 / 0.028)
- = 640.82 m/s
- Answer: 640.82 m/s
Worked example 2 (Standard)
Find the average kinetic energy of a gas molecule at 599 K.
- KE = (3/2)kT = 1.5 × 1.38 × 10⁻²³ × 599
- = 1.240e-20 J
- Answer: 1.240e-20 J
Worked example 3 (Challenge)
By what factor does the rms speed change if the absolute temperature becomes 9 times?
- v ∝ √T
- √9 = 3
- Answer: 3 times
Common mistakes and misconceptions
- Using g/mol
- Using °C
Practice questions
- (Basic) Find the rms speed of H₂ molecules at 506 K.
- (Basic) Find the rms speed of CO₂ molecules at 323 K.
- (Standard) Find the average kinetic energy of a gas molecule at 267 K.
- (Standard) Find the average kinetic energy of a gas molecule at 342 K.
- (Challenge) By what factor does the rms speed change if the absolute temperature becomes 16 times?
- (Challenge) By what factor does the rms speed change if the absolute temperature becomes 4 times?
Answer key with full working
- Q1: v = √(3 × 8.314 × 506 / 0.002) → = 2512.04 m/s → Answer: 2512.04 m/s
- Q2: v = √(3 × 8.314 × 323 / 0.044) → = 427.9 m/s → Answer: 427.9 m/s
- Q3: KE = (3/2)kT = 1.5 × 1.38 × 10⁻²³ × 267 → = 5.527e-21 J → Answer: 5.527e-21 J
- Q4: KE = (3/2)kT = 1.5 × 1.38 × 10⁻²³ × 342 → = 7.079e-21 J → Answer: 7.079e-21 J
- Q5: v ∝ √T → √16 = 4 → Answer: 4 times
- Q6: v ∝ √T → √4 = 2 → Answer: 2 times
Syllabus note
This skill is listed under "Kinetic Theory" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is rms speed of gas molecules in?
"Kinetic Theory", Class 11 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.