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General ScienceHard

The root mean square speed of the molecules of an ideal gas is given by the square root of

  1. A.RT divided by M
  2. B.2RT divided by M
  3. C.3RT divided by M
  4. D.8RT divided by pi M

Correct answer

C. 3RT divided by M

Explanation

The correct answer is C, 3RT divided by M. The root mean square speed follows from the kinetic gas equation and equals the square root of three RT divided by the molar mass, or equally the square root of three times the Boltzmann constant times the temperature divided by the mass of one molecule. B, 2RT divided by M under the root is the most probable speed, the speed possessed by the largest number of molecules. D, 8RT divided by pi M under the root is the average or mean speed. The three therefore stand in the ratio of the square root of two, the square root of eight over pi and the square root of three, so the most probable speed is the smallest and the root mean square speed the largest. A, RT divided by M is not any of the three standard speeds. Learning the order, most probable then average then root mean square, answers a whole family of questions.

Read the full article: Gas Laws and Kinetic Theory of Gases: Formulas and PYQs

Practice Questions

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Q1.General ScienceEasy

Boyle's law states that at constant temperature, the volume of a fixed mass of gas is

  1. A.Directly proportional to its pressure
  2. B.Inversely proportional to its pressure
  3. C.Independent of its pressure
  4. D.Proportional to the square of its pressure
Show answer
Correct answer: B. Inversely proportional to its pressure

Boyle's law, established in 1662, says that for a fixed mass of gas at constant temperature the product of pressure and volume stays constant, so doubling the pressure halves the volume.

Q2.General ScienceEasy

A hot air balloon rises because warm air

  1. A.Becomes denser than the surrounding air
  2. B.Expands and becomes less dense than the surrounding air
  3. C.Loses its mass on heating
  4. D.Has a lower specific heat than cold air
Show answer
Correct answer: B. Expands and becomes less dense than the surrounding air

By Charles's law the volume of a fixed mass of gas at constant pressure is proportional to its absolute temperature, so heating the air inside the envelope makes it expand; some of it escapes from the open mouth, the mass of air left inside falls, its density becomes lower than…

Q3.General ScienceEasy

Absolute zero of temperature is equal to

  1. A.0 degrees Celsius
  2. B.-100 degrees Celsius
  3. C.-273.15 degrees Celsius
  4. D.-373.15 degrees Celsius
Show answer
Correct answer: C. -273.15 degrees Celsius

Extending the straight line of Charles's law backwards shows that the volume of an ideal gas would become zero at minus 273.15 degrees Celsius, and this point is taken as the zero of the kelvin or absolute scale, at which molecular motion carries its least possible energy.

Q5.General ScienceMedium

The volume occupied by one mole of an ideal gas at 273.15 K and one atmosphere pressure is about

  1. A.11.2 litres
  2. B.22.4 litres
  3. C.44.8 litres
  4. D.1 litre
Show answer
Correct answer: B. 22.4 litres

Substituting one mole, 273.15 kelvin and one atmosphere in the ideal gas equation gives a volume of 22.4 litres, the molar volume at standard temperature and pressure, and this is the figure used in mole calculations; with the modern standard pressure of one bar the value works out to about…