Sure, let's analyze each pair of gases and select the one with the highest rate of effusion.
Effusion is the process in which gas molecules pass through a tiny opening from one container to another. According to Graham's law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
1. Oxygen ( [tex]\( \text{O}_2 \)[/tex] ) or Hydrogen ( [tex]\( \text{H}_2 \)[/tex] ):
- Molar mass of Oxygen ( [tex]\( \text{O}_2 \)[/tex] ) : 32 g/mol
- Molar mass of Hydrogen ( [tex]\( \text{H}_2 \)[/tex] ) : 2 g/mol
Because the rate of effusion is inversely proportional to the square root of the molar mass, the gas with the smaller molar mass ( [tex]\( \text{H}_2 \)[/tex] ) will have a higher rate of effusion.
Answer: [tex]\( \text{H}_2 \)[/tex]
[tex]\[ \boxed{H_2} \][/tex]
2. Methane ( [tex]\( \text{CH}_4 \)[/tex] ) or Carbon Tetrachloride ( [tex]\( \text{CCl}_4 \)[/tex] ):
- Molar mass of Methane ( [tex]\( \text{CH}_4 \)[/tex] ): 16 g/mol
- Molar mass of Carbon Tetrachloride ( [tex]\( \text{CCl}_4 \)[/tex] ): 154 g/mol
Similarly, the gas with the smaller molar mass ( [tex]\( \text{CH}_4 \)[/tex] ) will have a higher rate of effusion.
Answer: [tex]\( \text{CH}_4 \)[/tex]
[tex]\[ \boxed{CH_4} \][/tex]
3. Nitrogen ( [tex]\( \text{N}_2 \)[/tex] ) or Ammonia ( [tex]\( \text{NH}_3 \)[/tex] ):
- Molar mass of Nitrogen ( [tex]\( \text{N}_2 \)[/tex] ): 28 g/mol
- Molar mass of Ammonia ( [tex]\( \text{NH}_3 \)[/tex] ): 17 g/mol
Since the molar mass of [tex]\( \text{NH}_3 \)[/tex] is smaller than [tex]\( \text{N}_2 \)[/tex], [tex]\( \text{NH}_3 \)[/tex] will have a higher rate of effusion.
Answer: [tex]\( \text{NH}_3 \)[/tex]
[tex]\[ \boxed{NH_3} \][/tex]
4. Fluorine ( [tex]\( \text{F}_2 \)[/tex] ) or Chlorine ( [tex]\( \text{Cl}_2 \)[/tex] ):
- Molar mass of Fluorine ( [tex]\( \text{F}_2 \)[/tex] ): 38 g/mol
- Molar mass of Chlorine ( [tex]\( \text{Cl}_2 \)[/tex] ): 71 g/mol
The gas with the smaller molar mass ( [tex]\( \text{F}_2 \)[/tex] ) will have a higher rate of effusion.
Answer: [tex]\( \text{F}_2 \)[/tex]
[tex]\[ \boxed{F_2} \][/tex]
Thus, the answers are:
- Oxygen [tex]\( \left( O _2\right) \)[/tex] or hydrogen [tex]\( \left( H _2\right) \)[/tex]: [tex]\(\boxed{H_2}\)[/tex]
- Methane [tex]\( \left( CH _4\right) \)[/tex] or carbon tetrachloride [tex]\( \left( CCl _4\right) \)[/tex]: [tex]\(\boxed{CH_4}\)[/tex]
- Nitrogen [tex]\( \left( N_2\right) \)[/tex] or ammonia [tex]\( \left( NH_3\right) \)[/tex]: [tex]\(\boxed{NH_3}\)[/tex]
- Fluorine [tex]\( \left( F_2\right) \)[/tex] or chlorine [tex]\( \left( Cl_2\right) \)[/tex]: [tex]\(\boxed{F_2}\)[/tex]
