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A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.
- a)1.863
- b)0.7357
- c)0.5081
- d)1.8754
Correct answer is option 'C'. Can you explain this answer?
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A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelv...
Compressibility factor Z = PV/nRT; Z = 50 atm x (500/1000) ml / 2 x 0.082 x 300 k = 25/6×8.2 = 0.5081. That means Z < 1, so this is a negative deviation from ideal gas behaviour. So the gas is more compressible than expected.
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A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelv...
To calculate the compressibility factor of a gas, we can use the ideal gas equation and the van der Waals equation.
The ideal gas equation is given by:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/K·mol)
T = temperature (in Kelvin)
The van der Waals equation is a modification of the ideal gas equation that takes into account the volume of the gas molecules and the intermolecular forces. It is given by:
(P + an²/V²)(V - nb) = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
a and b are van der Waals constants specific to the gas
In this case, we are given:
n = 2 moles
V = 500 ml = 0.5 L
T = 300 K
P = 50 atm
We can first calculate the values of a and b for the gas using the van der Waals constants. The values for a and b can be found in the literature for different gases. For simplicity, let's assume that the gas in question is an ideal gas and does not have any intermolecular forces, so a = 0 and b = 0.
Using the ideal gas equation, we can calculate the expected pressure:
PV = nRT
50 atm * 0.5 L = 2 mol * 0.0821 L·atm/K·mol * 300 K
25 = 49.26
The calculated pressure is 49.26 atm, which is different from the given pressure of 50 atm. This indicates that the gas deviates from ideality and we need to use the compressibility factor to account for the deviation.
The compressibility factor, Z, is defined as the ratio of the actual volume of the gas to the volume predicted by the ideal gas law. It can be calculated using the equation:
Z = PV/RT
We can plug in the values we have to calculate the compressibility factor:
Z = (50 atm * 0.5 L) / (2 mol * 0.0821 L·atm/K·mol * 300 K)
Z = 0.5081
Therefore, the compressibility factor of the gas is approximately 0.5081, which matches with option C.
The ideal gas equation is given by:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/K·mol)
T = temperature (in Kelvin)
The van der Waals equation is a modification of the ideal gas equation that takes into account the volume of the gas molecules and the intermolecular forces. It is given by:
(P + an²/V²)(V - nb) = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
a and b are van der Waals constants specific to the gas
In this case, we are given:
n = 2 moles
V = 500 ml = 0.5 L
T = 300 K
P = 50 atm
We can first calculate the values of a and b for the gas using the van der Waals constants. The values for a and b can be found in the literature for different gases. For simplicity, let's assume that the gas in question is an ideal gas and does not have any intermolecular forces, so a = 0 and b = 0.
Using the ideal gas equation, we can calculate the expected pressure:
PV = nRT
50 atm * 0.5 L = 2 mol * 0.0821 L·atm/K·mol * 300 K
25 = 49.26
The calculated pressure is 49.26 atm, which is different from the given pressure of 50 atm. This indicates that the gas deviates from ideality and we need to use the compressibility factor to account for the deviation.
The compressibility factor, Z, is defined as the ratio of the actual volume of the gas to the volume predicted by the ideal gas law. It can be calculated using the equation:
Z = PV/RT
We can plug in the values we have to calculate the compressibility factor:
Z = (50 atm * 0.5 L) / (2 mol * 0.0821 L·atm/K·mol * 300 K)
Z = 0.5081
Therefore, the compressibility factor of the gas is approximately 0.5081, which matches with option C.
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A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.a)1.863b)0.7357c)0.5081d)1.8754Correct answer is option 'C'. Can you explain this answer?
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A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.a)1.863b)0.7357c)0.5081d)1.8754Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.a)1.863b)0.7357c)0.5081d)1.8754Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.a)1.863b)0.7357c)0.5081d)1.8754Correct answer is option 'C'. Can you explain this answer?.
A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.a)1.863b)0.7357c)0.5081d)1.8754Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.a)1.863b)0.7357c)0.5081d)1.8754Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A gas that is of 2 moles occupies a volume of about 500 ml at 300 Kelvin and 50 atmospheric pressure, calculate the compressibility factor of the gas.a)1.863b)0.7357c)0.5081d)1.8754Correct answer is option 'C'. Can you explain this answer?.
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