Question

the experimental apparatus represented above is used to demonstrate the rates at which gases diffuse. when the cotton - balls are placed in the ends of a tube at the same time, the gases diffuse from each end and meet somewhere in between, where they react to form a white solid. which of the following combinations will produce a solid closest to the center of the tube? a hcl and ch3nh2 b hcl and nh3 c hbr and ch3nh2 d hbr and nh3

Explanation:

Step1: Recall Graham's law

The rate of diffusion of a gas is inversely proportional to the square - root of its molar mass ($r\propto\frac{1}{\sqrt{M}}$). Gases with similar molar masses will diffuse at similar rates and meet closer to the center of the tube.

Step2: Calculate molar masses

• Molar mass of $HCl$: $M_{HCl}=1 + 35.5=36.5\ g/mol$.
• Molar mass of $HBr$: $M_{HBr}=1+ 79.9 = 80.9\ g/mol$.
• Molar mass of $NH_3$: $M_{NH_3}=14 + 3\times1=17\ g/mol$.
• Molar mass of $CH_3NH_2$: $M_{CH_3NH_2}=12 + 3\times1+14 + 2\times1=31\ g/mol$.

Step3: Analyze pairs

• For pair A ($HCl$ and $CH_3NH_2$): The molar - mass difference is $|36.5 - 31| = 5.5\ g/mol$.
• For pair B ($HCl$ and $NH_3$): The molar - mass difference is $|36.5 - 17|=19.5\ g/mol$.
• For pair C ($HBr$ and $CH_3NH_2$): The molar - mass difference is $|80.9 - 31| = 49.9\ g/mol$.
• For pair D ($HBr$ and $NH_3$): The molar - mass difference is $|80.9 - 17|=63.9\ g/mol$.

The pair with the smallest molar - mass difference is $HCl$ and $CH_3NH_2$.

Answer:

A. $HCl$ and $CH_3NH_2$