Question

The root-mean-square (RMS) speed of the molecules of a gas at 133°C is 189 m/s. Calculate the mass (m) of a single molecule in the gas.

A) 1.5×10^−26kg
B) 2.0×10 ^−26kg
C) 2.5×10 ^−26kg
D) 3.0×10 ^−26kg

Answer 1

The mass of a single molecule of a gas can be calculated from its RMS speed and the gas temperature using the formula relating RMS speed to the kinetic energy and temperature.

Step-by-step explanation:

The student is asking about the mass of a single molecule of gas based on its root-mean-square (RMS) speed at a given temperature. The RMS speed is related to the kinetic energy and temperature of the gas molecules. To find the mass of one molecule, we can use the formula Urms = √(3kBT/m), where Urms is the RMS speed, KB is the Boltzmann constant (1.38×10⁻²³ J/K), T is the absolute temperature in kelvin, and m is the mass of a single molecule. The absolute temperature in kelvin can be obtained by adding 273.15 to the Celsius temperature, giving us 133°C + 273.15 = 406.15 K. Plugging in the known values and solving for m, we should find the mass that corresponds with one of the provided options (A-D).