Respuesta :
Answer:
the final volume of the gas is [tex]V_2[/tex] = 1311.5 mL
Explanation:
Given that:
a sample gas has an initial volume of 61.5 mL
The workdone = 130.1 J
Pressure = 783 torr
The objective is to determine the final volume of the gas.
Since the process does 130.1 J of work on its surroundings at a constant pressure of 783 Torr. Then, the pressure is external.
Converting the external pressure to atm ; we have
External Pressure [tex]P_{ext}[/tex]:
[tex]P_{ext} = 783 \ torr \times \dfrac{1 \ atm}{760 \ torr}[/tex]
[tex]P_{ext} = 1.03 \ atm[/tex]
The workdone W = [tex]P_{ext}[/tex]V
The change in volume ΔV= [tex]\dfrac{W}{P_{ext}}[/tex]
ΔV = [tex]\dfrac{130.1 \ J \times \dfrac{1 \ L \ atm}{ 101.325 \ J} }{1.03 \ atm }[/tex]
ΔV = [tex]\dfrac{1.28398717 }{1.03 }[/tex]
ΔV = 1.25 L
ΔV = 1250 mL
Recall that the initial volume = 61.5 mL
The change in volume V is [tex]\Delta V = V_2 -V_1[/tex]
[tex]- V_2= - \Delta V -V_1[/tex]
multiply through by (-), we have:
[tex]V_2= \Delta V+V_1[/tex]
[tex]V_2[/tex] = 1250 mL + 61.5 mL
[tex]V_2[/tex] = 1311.5 mL
∴ the final volume of the gas is [tex]V_2[/tex] = 1311.5 mL
The final volume of the gas when the volume of 61.5 mL should be 1311.5 mL.
Calculation of the final volume:
Since
a sample gas has an initial volume of 61.5 mL
The workdone = 130.1 J
Pressure = 783 torr
So, here the external pressure should be
= 783 * 1 / 760
= 1.03 atm
Now the change in volume is
= 130.1 J * 1 / 101.325 J / 1.03
= 1250 mL
Now the change in volume should be
= 1250 + 61.5
= 1311.5 mL
hence, The final volume of the gas when the volume of 61.5 mL should be 1311.5 mL.
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