IDNLearn.com: Your trusted source for finding accurate and reliable answers. Ask anything and receive thorough, reliable answers from our community of experienced professionals.
Sagot :
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]
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]
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.
