Question

Calculate the root mean square for the atoms in a sample of helium gas at 25 degrees Celsius.

A) 1.0 m/s
B) 100 m/s
C) 500 m/s
D) 1000 m/s

Answer 1

The root mean square speed of helium atoms at 25 degrees Celsius is calculated to be approximately 1116.36 m/s, making option D (1000 m/s) the closest answer.

Step-by-step explanation:

To calculate the root mean square (rms) speed of helium atoms at a given temperature, we can use the following formula derived from the kinetic theory of gases:

• Urms = √(3kT/M)

where Urms is the root mean square speed, k is the Boltzmann constant (1.38 × 10-23 J/K), T is the temperature in Kelvin, and M is the molar mass of the gas in kilograms per mole.

First, convert the temperature from degrees Celsius to Kelvin:

• T = 25 °C + 273.15 = 298.15 K

Helium has a molar mass of 4.00 g/mol, which is 0.004 kg/mol in SI units. Plug in the values into the formula:

• Urms = √(3 × 1.38 × 10-23 J/K × 298.15 K / 0.004 kg/mol)

Calculate Urms:

• Urms ≈ √(1.24170 × 10-20 J/mol)
• Urms ≈ 1116.36 m/s

The closest answer to the calculated value is 1000 m/s, which is option D.