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In an ideal gas, the root mean square speed of the gas molecules is given by whi

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Question: In an ideal gas, the root mean square speed of the gas molecules is given by which of the following formulas?

Options:

  1. v_rms = √(3RT/M)
  2. v_rms = √(RT/M)
  3. v_rms = √(2RT/M)
  4. v_rms = √(R/M)

Correct Answer: v_rms = √(3RT/M)

Solution: 

The root mean square speed of gas molecules is given by the formula v_rms = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass.

In an ideal gas, the root mean square speed of the gas molecules is given by whi

Practice Questions

Q1
In an ideal gas, the root mean square speed of the gas molecules is given by which of the following formulas?
  1. v_rms = √(3RT/M)
  2. v_rms = √(RT/M)
  3. v_rms = √(2RT/M)
  4. v_rms = √(R/M)

Questions & Step-by-Step Solutions

In an ideal gas, the root mean square speed of the gas molecules is given by which of the following formulas?
  • Step 1: Understand that the root mean square speed (v_rms) is a way to measure the average speed of gas molecules in an ideal gas.
  • Step 2: Know that the formula for root mean square speed involves three important variables: R (the gas constant), T (the temperature in Kelvin), and M (the molar mass of the gas).
  • Step 3: The formula is written as v_rms = √(3RT/M).
  • Step 4: Recognize that R is a constant value (approximately 8.314 J/(mol·K)), T is the temperature of the gas, and M is the molar mass of the gas in kilograms per mole.
  • Step 5: To find the root mean square speed, you will plug in the values for R, T, and M into the formula and calculate the result.
  • Root Mean Square Speed – The root mean square speed (v_rms) is a measure of the average speed of gas molecules in an ideal gas, derived from kinetic theory.
  • Ideal Gas Law – The behavior of ideal gases is described by the ideal gas law, which relates pressure, volume, temperature, and number of moles.
  • Gas Constant – The gas constant (R) is a physical constant that appears in the equation of state for an ideal gas.
  • Molar Mass – Molar mass (M) is the mass of one mole of a substance, which affects the speed of gas molecules.
  • Temperature – Temperature (T) is a measure of the average kinetic energy of the gas molecules, influencing their speed.
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