Respuesta :
Answer:
The molar mass of B is 32.0 g/mol
The unknown gas might be O2 (option C)
Explanation:
Step 1: Data given
A sample of Xe takes 75 seconds to effuse out of a container.
An unknown gas takes 37 seconds to effuse out of the identical container
Molar mass Xe = 131.3 g/mol
Step 2:
Rate A / rate B = √ (MB/MA)
rate = amount / time
The equation includes rate, but you are given times. Since rate is amount/time, we have to invert that side of the equation.
Time B/Time A = √(MB/MA)
⇒with time B = the time the unknown gas needed to effuse = 37 seconds
⇒with time A = the time needed Xe needed to effuse = 75 seconds
⇒with MB = the molar mass of the unknown gas = TO BE DETERMINED
⇒ with MA = the molar mass of Xe = 131.3
37/75 = √ (MB/131.3)
MB = 32
The molar mass of B is 32.0 g/mol
The unknown gas might be O2
The most likely unknown gas has been [tex]\rm \bold{O_2}[/tex]. Thus, option C is correct.
The two gas required different times to be diffused from the same container. Thus, the rate of diffusion has been proportional to the molar mass of the substance.
Thus, the ratio of the rate of two samples can be given by:
[tex]\rm \dfrac{Rate\;of\;A}{Rate\;of\;B}\;=\;\dfrac{Molar\;mass\;of\;A}{Molar\;mass\;of\;B}[/tex]
Rate can be defined as the amount diffuses per unit time. The equation in terms of time can be given as:
[tex]\rm \dfrac{Time\;of\;B}{Time\;of\;A}\;=\;\sqrt{\dfrac{Molar\;mass\;of\;B}{Molar\;mass\;of\;A}}[/tex]
Let gas B be Xenon, having diffusion time 75 sec, and molar mass 131.3 g/mol
[tex]\rm \dfrac{75\;sec}{37\;sec}\;=\;\sqrt{\dfrac{131.3\;g/mol}{Molar\;mass\;of\;A}}[/tex]
Molar mass of A = 32 g/mol.
The gas with a molar mass of 32 g/mol has been oxygen. Thus, the most likely unknown gas has been [tex]\rm \bold{O_2}[/tex]. Thus, option C is correct.
For more information about the diffusion of gases, refer to the link:
https://brainly.com/question/879602
