Question

The root mean square velocity of hydrogen molecules at 300 Kelvin is 1930 meters per second. Then the rms velocity of oxygen molecules at 1200 Kelvin will be:

a) 2750 m/s
b) 3860 m/s
c) 5480 m/s
d) 7720 m/s

Answer 1

The rms velocity for oxygen molecules (O2) at 1200 K can be calculated using the kinetic theory of gases and the given information about hydrogen gas. However, after calculation, the resulting velocity does not match any of the given options, suggesting an error in the question.

Step-by-step explanation:

The root mean square (rms) velocity of any gas can be determined using the kinetic theory of gases, which relates the rms velocity (√Üᵢₗ), the temperature (T), and the molar mass (M) of the gas. This relationship is expressed by the formula √Üᵢₗ = √(3kT/M), where k is the Boltzmann constant and M is molar mass in kilograms per mole (kg/mol).

Given hydrogen molecules (H2) with rms velocity at 300 K is 1930 m/s and molar mass equal to 2.016 g/mol, we can find the rms velocity of oxygen molecules (O2) at 1200 K with molar mass equal to 32.0 g/mol by adjusting the formula accordingly.

Using the ratio of temperatures and molar masses for H2 and O2 gives us rms velocity for O2 (√ÜᵢₗO2):

√ÜᵢₗO2 = √ÜᵢₗH2 x √((TO2/TH2) x (MH2/MO2))

√ÜᵢₗO2 = 1930 m/s x √((1200/300) x (2.016/32.0))

√ÜᵢₗO2 = 1930 m/s x √(4 x 0.063))≈ 1930 m/s x √(0.252) ≈ 1930 m/s x 0.502 ≈ 969.06 m/s. However, as this answer is not an option, it seems there is an error in the question given.