A closed bulb of capacity 200ml containing CH4, H2, He at 300K. The ratio of partial pressure of CH4, H2, He, respectively, is 2:3:5. Calculate the ratio of partial pressure in the... A closed bulb of capacity 200ml containing CH4, H2, He at 300K. The ratio of partial pressure of CH4, H2, He, respectively, is 2:3:5. Calculate the ratio of partial pressure in the container.
Understand the Problem
The question is asking for the calculation of the partial pressures of three gases (CH4, H2, He) in a closed bulb based on their given ratio and the total capacity of the bulb. We will use the ideal gas law and the provided ratio of partial pressures to find the solution.
Answer
The partial pressures of the gases are: - \( P_{CH₄} = \frac{nRT}{6V} \), - \( P_{H₂} = \frac{nRT}{3V} \), - \( P_{He} = \frac{nRT}{2V} \)
Answer for screen readers
The partial pressures of the gases are given by:
- ( P_{CH₄} = \frac{nRT}{6V} )
- ( P_{H₂} = \frac{nRT}{3V} )
- ( P_{He} = \frac{nRT}{2V} )
Steps to Solve
- Identify the given information
We have the ratios of the gases and the total volume of the bulb. Let the partial pressures of CH₄, H₂, and He be proportional to their ratios, represented as ( x ), ( 2x ), and ( 3x ) respectively. The total pressure can be represented as: $$ P_{total} = x + 2x + 3x = 6x $$
- Use the ideal gas law
According to the ideal gas law, the total pressure in a closed system is given by: $$ P_{total} = \frac{nRT}{V} $$ Where:
- ( P_{total} ) is the total pressure,
- ( n ) is the total number of moles of gas,
- ( R ) is the universal gas constant,
- ( T ) is the temperature in Kelvin,
- ( V ) is the volume of the bulb.
We can equate the two expressions for ( P_{total} ): $$ 6x = \frac{nRT}{V} $$
- Calculate the partial pressures
From the total pressure equation, we can express ( x ) as: $$ x = \frac{nRT}{6V} $$
Now we can find the individual partial pressures:
- For CH₄: ( P_{CH₄} = x = \frac{nRT}{6V} )
- For H₂: ( P_{H₂} = 2x = \frac{2nRT}{6V} = \frac{nRT}{3V} )
- For He: ( P_{He} = 3x = \frac{3nRT}{6V} = \frac{nRT}{2V} )
- Final expressions for partial pressures
The final expressions for the partial pressures are:
- ( P_{CH₄} = \frac{nRT}{6V} )
- ( P_{H₂} = \frac{nRT}{3V} )
- ( P_{He} = \frac{nRT}{2V} )
The partial pressures of the gases are given by:
- ( P_{CH₄} = \frac{nRT}{6V} )
- ( P_{H₂} = \frac{nRT}{3V} )
- ( P_{He} = \frac{nRT}{2V} )
More Information
This setup is based on Dalton's Law of Partial Pressures, which states that in a mixture of gases, the total pressure is equal to the sum of the partial pressures of the individual gases. The ratios provided allow us to relate the pressures of different gases in a consistent manner.
Tips
Common mistakes include:
- Confusing the ratios of gases and their respective partial pressures.
- Forgetting to convert the ratios into the actual form required for calculations or miscalculating the total pressure.
- Not recognizing that the ideal gas law applies equally to each component in the mixture, leading to confusion in separating the components.
