Question

Calculate the root mean square for the atoms in a sample of helium gas at 25 degrees Celsius. What is the molar mass?

A) 4 g/mol
B) 8 g/mol
C) 12 g/mol
D) 16 g/mol

Answer 1

The root mean square speed of helium atoms in a sample can be calculated using the RMS speed equation. The molar mass of helium is 4 g/mol.

Step-by-step explanation:

The root mean square (rms) speed of atoms in a sample of gas can be calculated using the equation:

rms speed = sqrt((3 * R * T) / M)

where R is the ideal gas constant (0.0821 L * atm / (mol * K)), T is the temperature in Kelvin, and M is the molar mass of the gas in g/mol.

For helium gas at 25 degrees Celsius, we need to convert the temperature to Kelvin by adding 273, so T = 25 + 273 = 298 K. The molar mass of helium is 4 g/mol. Plugging these values into the equation:

rms speed = sqrt((3 * 0.0821 * 298) / 4) = ~193.3 m/s

Therefore, the root mean square speed of the helium atoms in the sample is approximately 193.3 m/s.

Option A) 4 g/mol is the correct molar mass for helium.