
Calculate the root mean square, average and most probable speed of oxygen at .
Answer
482.1k+ views
Hint: Using the Maxwell distribution of molecular velocities, we have three types of molecular speeds. They are most probable speed, average speed and root mean square speed.
Complete step by step answer:
-Most probable speed is the speed possessed by the maximum number of molecules of a gas at a given temperature. The formula to find out most probable speed is,
Most probable speed,
Where, R is the universal gas constant. Its value is .
T is the temperature in Kelvin.
M is the molar mass of a gas molecule in kg.
-Average speed is the arithmetic mean of different speeds possessed by the molecules of a gas at a given temperature. The formula for average speed is,
Average speed,
-Root mean square speed is the square root of the mean of the squares of different speeds possessed by molecules of a gas at a given temperature. The formula for root mean square speed is,
Root mean square speed,
-We need to calculate the root mean square, average and most probable speed of oxygen at .
We know, molar mass of oxygen
Given, temperature =
Now let us find out the speeds by substituting the values to the above equations.
Most probable speed,
Average speed,
-Root mean square speed,
-Hence the values of the root mean square, average and most probable speed of oxygen are and respectively.
Note:
We can use a simple formula for finding the three velocities. First we need to calculate the most probable speed using the above equation. Then we can calculate average speed and root mean square speed using the ratio, .
Complete step by step answer:
-Most probable speed is the speed possessed by the maximum number of molecules of a gas at a given temperature. The formula to find out most probable speed is,
Most probable speed,
Where, R is the universal gas constant. Its value is
T is the temperature in Kelvin.
M is the molar mass of a gas molecule in kg.
-Average speed is the arithmetic mean of different speeds possessed by the molecules of a gas at a given temperature. The formula for average speed is,
Average speed,
-Root mean square speed is the square root of the mean of the squares of different speeds possessed by molecules of a gas at a given temperature. The formula for root mean square speed is,
Root mean square speed,
-We need to calculate the root mean square, average and most probable speed of oxygen at .
We know, molar mass of oxygen
Given, temperature =
Now let us find out the speeds by substituting the values to the above equations.
Most probable speed,
Average speed,
-Root mean square speed,
-Hence the values of the root mean square, average and most probable speed of oxygen are
Note:
We can use a simple formula for finding the three velocities. First we need to calculate the most probable speed using the above equation. Then we can calculate average speed and root mean square speed using the ratio,
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
A deep narrow valley with steep sides formed as a result class 12 biology CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Derive an expression for electric potential at point class 12 physics CBSE
