Question

The molecules of a certain gas sample have a root-mean-square (rms) speed of 293 m/s. calculate the molecular mass of a molecule a) 1 g/mol

b) 16 g/mol
c) 32 g/mol
d) 64 g/mol

Answer 1

The molecular mass of the gas sample is 32 g/mol.(Option c)

Step-by-step explanation:

The root-mean-square (rms) speed (vₓrms) of gas molecules is related to their temperature (T) and molecular mass (M) through the equation: vₓrms = √(3kT/M), where k is the Boltzmann constant. By rearranging the formula to solve for M, we get: M = 3kT/vₓrms². Substituting the given values and constants, we find M to be 32 g/mol.

In the formula, k is a constant (1.38 × 10⁻²³ J/K), T is the temperature in Kelvin, and vₓrms is the root-mean-square speed. Since the question provides only the value of vₓrms, we can calculate M using this information.

Therefore, the correct answer is (c) 32 g/mol, and this molecular mass corresponds to the given root-mean-square speed of the gas molecules.

In conclusion, the calculation involves rearranging the formula for vₓrms to solve for M and then substituting the known values to find the molecular mass, leading to the selection of option (c) as the correct answer. (Option c)