Respuesta :
Answer:The change in temperature of the gas mixture is -68.44 K.
Explanation:
1. Temperature of the bottle when only helium gas was present :T
Pressure inside the container =P= 1.83 atm
Volume of the container = V = 2.50 L
Moles of helium gas = n = 0.458 moles
Using an Ideal gas equation:
[tex]PV=nRT[/tex]
[tex]T=\frac{PV}{nR}=\frac{1.83 atm\times 2.50 L}{0.458 mol\times 0.0820 atm L/mol K}=121.81 K[/tex]
2. Temperature of the bottle when argon gas is added into the container:T'
Pressure inside the container = P' =2.05 atm
Volume of the container = V = 2.50 L
Moles of helium gas = n' = 0.458 mol + 0.713 mol = 1.171 mol
[tex]P'V=n'RT'[/tex]
[tex]T'=\frac{P'V}{n'R}=\frac{2.05 atm\times 2.50 L}{1.171 mol\times 0.0820 atm L/mol K}=53.37 K[/tex]
The change in temperature will be given as:
Final temperature = Initial temperature:T' - T
53.37 k - 121.81 K = -68.44 K
The change in temperature of the gas mixture is -68.44 K.
The temperature of the bottle has been dropped by 68.29 K, and the final temperature of the bottle has been 53.385 K.
The gas has been assumed to be an ideal gas. Thus according to the ideal gas equation:
PV = nRT
P = Pressure of He gas = 1.83 atm
V = Volume of He gas = 2.50 L
n = moles of gas = 0.458
R = constant = 0.0821
T = temperature
The temperature of the bottle in the presence of He gas has been:
1.83 [tex]\times[/tex] 2.50 = 0.458 [tex]\times[/tex] 0.0821 [tex]\times[/tex] Temperature
4.575 = 0.0376 Temperature
Temperature = 121.675 K.
On the addition of Argon (0.713 mol)
n = 0.713 + 0.458 mol
n = 1.171 mol
The pressure of the bottle has been increased to 2.05 atm.
P = 2.05 atm
Substituting the values, the temperature of the bottle after the addition of Argon:
2.05 [tex]\times[/tex] 2.50 = 1.171 [tex]\times[/tex] 0.0821 [tex]\times[/tex] Temperature
5.125 = 0.096 Temperature
Temperature = 53.385 K.
The change in temperature can be given by:
Change in temperature = Final temperature - Initial temperature
Change in temperature = 53.385 K - 121.675 K
Change in temperature = -68.29 K
The temperature of the bottle has been dropped by 68.29 K, and the final temperature of the bottle has been 53.385 K.
For more information about the change in temperature, refer to the link:
https://brainly.com/question/13945683
