A closed container with a volume of 8000cm^3 is filled with Xenon gas. the temperature is 273K and the pressure is 2 atm. How many moles of Xenon are in the container?

Question

A closed container with a volume of 8000cm^3 is filled with Xenon gas. the temperature is 273K and the pressure is 2 atm. How many moles of Xenon are in the container?

The container is now submerged in boiling water until the gas inside the container is at 373K. What is the pressure of the Xenon?

Thanks for your help.

Answer 1

V=8000cm³=8•10⁻³m³

p=2 atm= 2.03•10⁵Pa
T=273 K

ν=pV/RT = 2.03•10⁵•8•10⁻³/273•8.31 =
= 0.716 moles

V=const
p₁/T₁=p/T
p₁=T₁p/T=373•2.03•10⁵/273 =2.77•10⁵Pa

Answer 2

To find the number of moles of Xenon in the container, we can use the ideal gas law equation, which is:

PV = nRT

Where:
P is the pressure of the gas in atm (atmospheres)
V is the volume of the gas in liters
n is the number of moles of gas
R is the ideal gas constant, which is 0.0821 L.atm/mol.K
T is the temperature of the gas in Kelvin

Let's calculate the number of moles of Xenon in the container.

Given:
P = 2 atm
V = 8000 cm^3 (which is equivalent to 8 L since 1 L = 1000 cm^3)
T = 273 K

First, we need to convert the volume from cm^3 to L:
V = 8000 cm^3 = 8000 cm^3 / 1000 cm^3/L = 8 L

Now we can plug these values into the ideal gas law equation:

PV = nRT

(2 atm) * (8 L) = n * (0.0821 L.atm/mol.K) * (273 K)

16 atm.L = n * 22.41 L.atm/mol

To solve for n (the number of moles), we divide both sides of the equation by 22.41 L.atm/mol:

n = (16 atm.L) / (22.41 L.atm/mol)

n ≈ 0.714 moles

Therefore, there are approximately 0.714 moles of Xenon gas in the container.

Now, let's determine the pressure of the Xenon when the temperature is increased to 373K.

To find the new pressure, we can rearrange the ideal gas law equation:

P1V1 / T1 = P2V2 / T2

Where:
P1 and T1 are the initial pressure and temperature respectively
P2 and T2 are the final pressure and temperature respectively
V1 and V2 are the same volume in this case

Let's plug in the values we know:

P1 = 2 atm
T1 = 273 K
T2 = 373 K
V1 = 8 L
V2 = 8 L

(2 atm) * (8 L) / (273 K) = P2 * (8 L) / (373 K)

16 atm.L / 273 K = P2 * 8 L / 373 K

To find P2, we can rearrange the equation:

P2 = (16 atm.L / 273 K) * (373 K / 8 L)

P2 ≈ 1.781 atm

Therefore, when the gas inside the container reaches a temperature of 373K, the pressure of the Xenon gas will be approximately 1.781 atm.