Consider a container with a frictionless piston that contains a given amount of CO₂ Assume that the behavior of this gas can be described by the van der Waals equation of state For carbon dioxide gas (CO₂), the constants in the van der Waals equation are a=0.364 J-m³/mol and b 4.27 x 10 m³/mol. Let's assume that initially the external pressure is 22.0 bar, which is the sum of a 1 bar atmospheric pressure and the pressure created by a very large number of very small pebbles that rest on top of the piston. The initial volume of gas is 0.5 L and the initial temperature is 25°C. Now, you will increase the volume of the gas by changing the external pressure slowly in a way that guarantees that the temperature of the system remains constant throughout the process. To do this, imagine you remove the pebbles one by one slowly to increase the volume by an infinitesimal amount. Every time you remove a weight you allow the system to equilibrate. Your cylinder is immersed in a water bath at 25°C, which keeps your gas at the same temperature throughout the whole process. Remember to use three significant figures for all numerical answers. The margin of error foreach (non-trivial) numerical answer is 1%. To avoid rounding errors use the unrounded intermediate values in your final calculations.
Consider a container with a frictionless piston that contains a given amount of CO₂ Assume that the behavior of this gas can be described by the van der Waals equation of state For carbon dioxide gas (CO₂), the constants in the van der Waals equation are a=0.364 J-m³/mol and b 4.27 x 10 m³/mol. Let's assume that initially the external pressure is 22.0 bar, which is the sum of a 1 bar atmospheric pressure and the pressure created by a very large number of very small pebbles that rest on top of the piston. The initial volume of gas is 0.5 L and the initial temperature is 25°C. Now, you will increase the volume of the gas by changing the external pressure slowly in a way that guarantees that the temperature of the system remains constant throughout the process. To do this, imagine you remove the pebbles one by one slowly to increase the volume by an infinitesimal amount. Every time you remove a weight you allow the system to equilibrate. Your cylinder is immersed in a water bath at 25°C, which keeps your gas at the same temperature throughout the whole process. Remember to use three significant figures for all numerical answers. The margin of error foreach (non-trivial) numerical answer is 1%. To avoid rounding errors use the unrounded intermediate values in your final calculations.
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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![Consider a container with a frictionless piston that contains a given amount of CO₂-
Assume that the behavior of this gas can be described by the van der Waals equation
of state.
For carbon dioxide gas (CO₂), the constants in the van der Waals equation are
a=0.364 J- m³/mol and b=4.27 x 10 m³/mol.
-5
Let's assume that initially the external pressure is 22.0 bar, which is the sum of a 1 bar
atmospheric pressure and the pressure created by a very large number of very small
pebbles that rest on top of the piston. The initial volume of gas is 0.5 L and the initial
temperature is 25°C.
Now, you will increase the volume of the gas by changing the external pressure slowly
in a way that guarantees that the temperature of the system remains constant
throughout the process. To do this, imagine you remove the pebbles one by one
slowly to increase the volume by an infinitesimal amount. Every time you remove a
weight you allow the system to equilibrate. Your cylinder is immersed in a water bath
at 25°C, which keeps your gas at the same temperature throughout the whole
process.
Remember to use three significant figures for all numerical answers. The margin of
error foreach (non-trivial) numerical answer is 1%. To avoid rounding errors use the
unrounded intermediate values in your final calculations.
▼
Part A
How many mols of CO₂ are in the container? (you may find this website useful: http://www.1728.org/cubic.htm)
Check your results for consistency with the provided information, before you enter them below. The error margin is 2%.
n =
Submit
Part B
Submit
▾ Part C
ΕΠΙΑΣΦΗ
Request Answer
What is the volume of the gas when you remove all pebbles? (also here, you may find this website useful: http://www.1728.org/cubic.htm, but you can also get very close to the correct answer without
it)
Check your results for consistency with the provided information, before you enter them below.
VE ΑΣΦ 3 @ C
Submit
Request Answer
What is the final pressure of the gas?
VE] ΑΣΦ 1
CE ?
Request Answer
?
mol
?
L
bar](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ea18822-caa6-41c2-875c-b394b4bd2109%2Fe6523624-76bf-449c-ae9e-efd453b12c29%2Fpp8gkn8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a container with a frictionless piston that contains a given amount of CO₂-
Assume that the behavior of this gas can be described by the van der Waals equation
of state.
For carbon dioxide gas (CO₂), the constants in the van der Waals equation are
a=0.364 J- m³/mol and b=4.27 x 10 m³/mol.
-5
Let's assume that initially the external pressure is 22.0 bar, which is the sum of a 1 bar
atmospheric pressure and the pressure created by a very large number of very small
pebbles that rest on top of the piston. The initial volume of gas is 0.5 L and the initial
temperature is 25°C.
Now, you will increase the volume of the gas by changing the external pressure slowly
in a way that guarantees that the temperature of the system remains constant
throughout the process. To do this, imagine you remove the pebbles one by one
slowly to increase the volume by an infinitesimal amount. Every time you remove a
weight you allow the system to equilibrate. Your cylinder is immersed in a water bath
at 25°C, which keeps your gas at the same temperature throughout the whole
process.
Remember to use three significant figures for all numerical answers. The margin of
error foreach (non-trivial) numerical answer is 1%. To avoid rounding errors use the
unrounded intermediate values in your final calculations.
▼
Part A
How many mols of CO₂ are in the container? (you may find this website useful: http://www.1728.org/cubic.htm)
Check your results for consistency with the provided information, before you enter them below. The error margin is 2%.
n =
Submit
Part B
Submit
▾ Part C
ΕΠΙΑΣΦΗ
Request Answer
What is the volume of the gas when you remove all pebbles? (also here, you may find this website useful: http://www.1728.org/cubic.htm, but you can also get very close to the correct answer without
it)
Check your results for consistency with the provided information, before you enter them below.
VE ΑΣΦ 3 @ C
Submit
Request Answer
What is the final pressure of the gas?
VE] ΑΣΦ 1
CE ?
Request Answer
?
mol
?
L
bar
Transcribed Image Text:Part E
Calculate the work Wedr due to this reversible, isothermal expansion of the real gas.
Keep in mind not to use an equation blindly. Go through the individual steps, starting with the force against which the work is being carried out (don't forget the pebbles). Get ready for
some more serious integration.
Hint: Formulate the answer as an integral over the volume change dV instead of the change of the piston position dh.
Wodw
15| ΑΣΦ
?
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