A sample of an ideal gas in a cylinder of volume 3.49 L at 298 K and 2.67 atm expands to 8.15 L by two different pathways. Path A is an isothermal, reversible expansion. Path B has two steps. In the first step, the gas is cooled at constant volume to 1.23 atm . In the second step, the gas is heated and allowed to expand against a constant external pressure of 1.23 atm until the final volume is 8.15 L .
Calculate the work for path A
Calculate the work for path B
can someone please walk through the steps using the numbers given? Ive tried looking at other chem community posts and I try doing what they say, but i still keep getting the wrong answer
Acheive #14
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Re: Acheive #14
a) I had different numbers but first you have to calculate the number of moles by using n = PV / RT so n = 2.67(3.49)/(8.206 x 10^-2)(298). The question tells you this is an isothermal and reversible reaction so you use the equation w = -nRT(ln(VF/Vi)) to find the work done. For work, you need to use 8.314 J /(mol x K) as the value of R to make sure your units line up.
b) For path B, it occurs in 2 steps. In the first step, we are told the volume is constant so the work done is 0. In the second step, we use the equation w = -(external pressure)(change in volume). This is w = -1.23(8.15 -3.49) which gives you an answer in L x atm. To get the answer in J, multiply this value by 101.325 J / (1 L x atm).
b) For path B, it occurs in 2 steps. In the first step, we are told the volume is constant so the work done is 0. In the second step, we use the equation w = -(external pressure)(change in volume). This is w = -1.23(8.15 -3.49) which gives you an answer in L x atm. To get the answer in J, multiply this value by 101.325 J / (1 L x atm).
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Re: Acheive #14
Jacqueline Wheeler 3I wrote:a) I had different numbers but first you have to calculate the number of moles by using n = PV / RT so n = 2.67(3.49)/(8.206 x 10^-2)(298). The question tells you this is an isothermal and reversible reaction so you use the equation w = -nRT(ln(VF/Vi)) to find the work done. For work, you need to use 8.314 J /(mol x K) as the value of R to make sure your units line up.
b) For path B, it occurs in 2 steps. In the first step, we are told the volume is constant so the work done is 0. In the second step, we use the equation w = -(external pressure)(change in volume). This is w = -1.23(8.15 -3.49) which gives you an answer in L x atm. To get the answer in J, multiply this value by 101.325 J / (1 L x atm).
How do you know to use 3.49L for V in PV=nRT? Why not 8.15 or (8.15-3.49)?
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Re: Acheive #14
The problem tells you it is an ideal gas under these conditions: volume = 3.49 L at 298 K and 2.67 atm. So you can use the ideal gas law equation to find the number of moles using these given values. You would account for the change of volume when you calculate the work done by the system.
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