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In Adiabatic expansion of a mixture of 2 volumes of hydrogen and 1 volume of oxygen from 320 ml to 10 ml caused explosion. The initial pressure and temperature of the gaseous mixture were 1 atm and 27°C.
What is pressure of gaseous mixture at the moment of explosion?
- a)32 atm
- b)128 atm
- c)1/32 atm
- d)1/128 atm
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In Adiabatic expansion of a mixture of 2 volumes of hydrogen and 1 vo...
Using ideal gas equation at constant temperature and number of moles we can apply the expression
P1V1γ = P2V2γ
P1 = 1 atm
V1 = 320 ml
V2 = 10 ml
= 128 atm
Therefore, the pressure of gaseous mixture at the moment of explosion is 128 atm.
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In Adiabatic expansion of a mixture of 2 volumes of hydrogen and 1 vo...
Solution:
Given:
Initial volume of hydrogen = 2 volumes
Initial volume of oxygen = 1 volume
Final volume of the mixture = 10 ml
Step 1: Find the final volumes of hydrogen and oxygen.
Since the mixture is in the ratio of 2:1, the final volumes of hydrogen and oxygen can be calculated as follows:
Final volume of hydrogen = (2/3) * final volume of the mixture = (2/3) * 10 ml = 6.67 ml
Final volume of oxygen = (1/3) * final volume of the mixture = (1/3) * 10 ml = 3.33 ml
Step 2: Use the ideal gas equation to find the final pressure of the mixture.
The ideal gas equation is given by:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the expansion is adiabatic, there is no heat exchange with the surroundings and thus no change in the number of moles of the gases.
Step 3: Convert the initial temperature from Celsius to Kelvin.
Initial temperature = 27°C = 27 + 273 = 300 K
Step 4: Calculate the initial number of moles.
The initial number of moles can be calculated using the ideal gas equation:
PV = nRT
n = PV / RT
= (1 atm * 320 ml) / (0.0821 atm L/mol K * 300 K)
= 0.0135 mol
Step 5: Calculate the final pressure of the mixture.
Since the number of moles remains constant, we can use the ideal gas equation to calculate the final pressure:
P1V1 / T1 = P2V2 / T2
Where:
P1 = initial pressure = 1 atm
V1 = initial volume = 320 ml = 0.32 L
T1 = initial temperature = 300 K
P2 = final pressure (to be determined)
V2 = final volume = 10 ml = 0.01 L
T2 = final temperature (since the expansion is adiabatic, the final temperature is not given)
P2 = (P1V1T2) / (V2T1)
= (1 atm * 0.32 L * T2) / (0.01 L * 300 K)
= 32 atm
Therefore, the pressure of the gaseous mixture at the moment of explosion is 32 atm, which corresponds to option (b).
Given:
Initial volume of hydrogen = 2 volumes
Initial volume of oxygen = 1 volume
Final volume of the mixture = 10 ml
Step 1: Find the final volumes of hydrogen and oxygen.
Since the mixture is in the ratio of 2:1, the final volumes of hydrogen and oxygen can be calculated as follows:
Final volume of hydrogen = (2/3) * final volume of the mixture = (2/3) * 10 ml = 6.67 ml
Final volume of oxygen = (1/3) * final volume of the mixture = (1/3) * 10 ml = 3.33 ml
Step 2: Use the ideal gas equation to find the final pressure of the mixture.
The ideal gas equation is given by:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the expansion is adiabatic, there is no heat exchange with the surroundings and thus no change in the number of moles of the gases.
Step 3: Convert the initial temperature from Celsius to Kelvin.
Initial temperature = 27°C = 27 + 273 = 300 K
Step 4: Calculate the initial number of moles.
The initial number of moles can be calculated using the ideal gas equation:
PV = nRT
n = PV / RT
= (1 atm * 320 ml) / (0.0821 atm L/mol K * 300 K)
= 0.0135 mol
Step 5: Calculate the final pressure of the mixture.
Since the number of moles remains constant, we can use the ideal gas equation to calculate the final pressure:
P1V1 / T1 = P2V2 / T2
Where:
P1 = initial pressure = 1 atm
V1 = initial volume = 320 ml = 0.32 L
T1 = initial temperature = 300 K
P2 = final pressure (to be determined)
V2 = final volume = 10 ml = 0.01 L
T2 = final temperature (since the expansion is adiabatic, the final temperature is not given)
P2 = (P1V1T2) / (V2T1)
= (1 atm * 0.32 L * T2) / (0.01 L * 300 K)
= 32 atm
Therefore, the pressure of the gaseous mixture at the moment of explosion is 32 atm, which corresponds to option (b).
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In Adiabatic expansion of a mixture of 2 volumes of hydrogen and 1 volume of oxygen from 320 ml to 10 ml caused explosion. The initial pressure and temperature of the gaseous mixture were 1 atm and 27°C.What is pressure of gaseous mixture at the moment of explosion?a)32 atmb)128 atmc)1/32 atmd)1/128 atmCorrect answer is option 'B'. Can you explain this answer?
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