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A vessel has 10 g of hydrogen gas at pressure P and temperature 400 K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure becomes half and temperature becomes 3/4th of its previous value?
- a)1 g
- b)3/4g
- c)10/3g
- d)14/4 g
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A vessel has 10 g of hydrogen gas at pressure P and temperature 400 K...
Given information:
- Initial pressure (P) of the hydrogen gas = P
- Initial temperature (T) of the hydrogen gas = 400 K
- Final pressure (Pf) = P/2
- Final temperature (Tf) = 3/4 * T
Using the ideal gas law:
The ideal gas law states that the product of pressure (P), volume (V), and temperature (T) of a gas is proportional to the number of moles of the gas (n) and the universal gas constant (R).
PV = nRT
Step 1: Calculating the initial number of moles of hydrogen gas:
Since the volume is not given, we can assume that it remains constant throughout the process. Therefore, the initial number of moles (n1) of hydrogen gas can be calculated using the initial pressure (P), temperature (T), and the ideal gas constant (R).
n1 = PV/RT
Step 2: Calculating the final number of moles of hydrogen gas:
Using the final pressure (Pf), final temperature (Tf), and the same volume, we can calculate the final number of moles (n2) of hydrogen gas.
n2 = PfV/RTf
Step 3: Calculating the amount of hydrogen gas leaked:
The amount of hydrogen gas leaked is equal to the difference between the initial and final number of moles.
Leaked amount = n1 - n2
Step 4: Substituting the given values:
Substituting the given values into the equations, we have:
n1 = (P * V) / (R * T)
n2 = (Pf * V) / (R * Tf)
Leaked amount = n1 - n2
Step 5: Simplifying the equation:
Substituting the values of n1 and n2, we get:
Leaked amount = ((P * V) / (R * T)) - ((Pf * V) / (R * Tf))
Step 6: Canceling out the common terms:
The volume (V) and the ideal gas constant (R) are common in both terms. Therefore, they can be canceled out.
Leaked amount = (P / T) - (Pf / Tf)
Step 7: Substituting the given values:
Substituting the given values of P, Pf, T, and Tf, we have:
Leaked amount = (P / T) - (P/2) / (3/4 * T)
Step 8: Simplifying the equation:
Simplifying the equation, we get:
Leaked amount = (4P/T) - (2P/3T)
Leaked amount = (12P - 2P) / 3T
Leaked amount = 10P / 3T
Step 9: Substituting the initial values:
Substituting the initial pressure (P) and temperature (T) values, we get:
Leaked amount = 10P / 3T
Leaked amount = 10 * P / (3 * 400)
Leaked amount = P / 120
Step 10
- Initial pressure (P) of the hydrogen gas = P
- Initial temperature (T) of the hydrogen gas = 400 K
- Final pressure (Pf) = P/2
- Final temperature (Tf) = 3/4 * T
Using the ideal gas law:
The ideal gas law states that the product of pressure (P), volume (V), and temperature (T) of a gas is proportional to the number of moles of the gas (n) and the universal gas constant (R).
PV = nRT
Step 1: Calculating the initial number of moles of hydrogen gas:
Since the volume is not given, we can assume that it remains constant throughout the process. Therefore, the initial number of moles (n1) of hydrogen gas can be calculated using the initial pressure (P), temperature (T), and the ideal gas constant (R).
n1 = PV/RT
Step 2: Calculating the final number of moles of hydrogen gas:
Using the final pressure (Pf), final temperature (Tf), and the same volume, we can calculate the final number of moles (n2) of hydrogen gas.
n2 = PfV/RTf
Step 3: Calculating the amount of hydrogen gas leaked:
The amount of hydrogen gas leaked is equal to the difference between the initial and final number of moles.
Leaked amount = n1 - n2
Step 4: Substituting the given values:
Substituting the given values into the equations, we have:
n1 = (P * V) / (R * T)
n2 = (Pf * V) / (R * Tf)
Leaked amount = n1 - n2
Step 5: Simplifying the equation:
Substituting the values of n1 and n2, we get:
Leaked amount = ((P * V) / (R * T)) - ((Pf * V) / (R * Tf))
Step 6: Canceling out the common terms:
The volume (V) and the ideal gas constant (R) are common in both terms. Therefore, they can be canceled out.
Leaked amount = (P / T) - (Pf / Tf)
Step 7: Substituting the given values:
Substituting the given values of P, Pf, T, and Tf, we have:
Leaked amount = (P / T) - (P/2) / (3/4 * T)
Step 8: Simplifying the equation:
Simplifying the equation, we get:
Leaked amount = (4P/T) - (2P/3T)
Leaked amount = (12P - 2P) / 3T
Leaked amount = 10P / 3T
Step 9: Substituting the initial values:
Substituting the initial pressure (P) and temperature (T) values, we get:
Leaked amount = 10P / 3T
Leaked amount = 10 * P / (3 * 400)
Leaked amount = P / 120
Step 10
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A vessel has 10 g of hydrogen gas at pressure P and temperature 400 K...
Let x g gas leaks out
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A vessel has 10 g of hydrogen gas at pressure P and temperature 400 K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure becomes half and temperature becomes 3/4th of its previous value?a)1 gb)3/4gc)10/3gd)14/4 gCorrect answer is option 'C'. Can you explain this answer?
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