Question

In a sample of hydrogen sulfide (M=34.1g/mol) at a temperature of 3.00×10² K, estimate the ratio of the number of molecules that have speeds very close to vrms to the number that have speeds very close to 2vrms.

a) 1:1
b) 2:1
c) 1:2
d) 1:4

Answer 1

The ratio of hydrogen sulfide molecules with speeds at Vrms to those at 2Vrms is significantly greater than 1, as described by the Maxwell-Boltzmann distribution of molecular speeds, which indicates fewer molecules will reach higher speeds like 2Vrms.

Step-by-step explanation:

To estimate the ratio of the number of hydrogen sulfide (H2S) molecules with speeds very close to Vrms to the number with speeds very close to 2Vrms, we can consider the Maxwell-Boltzmann distribution of molecular speeds. This distribution shows that the number of molecules with a given speed drops sharply as the speed increases.

Therefore, far fewer molecules will have speeds of 2Vrms compared to Vrms.

Without specific distribution data or a more detailed model, we cannot calculate the exact ratio, but it is evident that the ratio of molecules with a speed of Vrms to those with 2Vrms is greater than 1. If an approximation such as the square root of e over 3 can be used for a similar problem, we might surmise that the ratio is along those lines, meaning that there are significantly more molecules at Vrms than at 2Vrms.