Calculating Pressure and Temperature in a Container of Argon Gas

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In summary, to find the pressure and temperature inside a container of argon gas, we can use the equations p=(1/3)(N/V)mv^2 and pV=NKbT. By finding the number of moles in the container (24.9 moles) and the molar mass of argon (40g/mol), we can calculate the mass of the gas (0.9968 kg) and plug it into the equations to solve for pressure and temperature. By using the equation Vrms=(3KbT/m)^1/2 and the mass of one argon atom (6.627E-26), we can calculate the rms speed of the atoms and use that to find the pressure.
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gsharples12
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The number density in a container of argon gas is 1.50×10e25 . The atoms are moving with an rms speed of 465 . What are (a) the pressure and (b) the temperature inside the container?

Vrms=(3KbT/m)^1/2

Na = 6.02X10^23 particles/mol

Ar=40u

p=F/A=(1/3)(N/V)mv^2

pV=NKbT


I started off with finding out how many moles there were in the container by taking 1.5e25 and dividing that by 6.02e23 and got 24.9 moles. I looked up Molar mass for Ar and got 40g per mol. The mass of the Ar is .9968 kg.

Then I am plugging what I found for m into the first equation to solve for T but the number for T doesn't look right. Am I on the right track?
 
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  • #2
So I figured out that 1 atom of Ar = 6.627E-26 and pluged it into p=(1/3)(N/V)mv^2
and got the correct answer for Pressure.
 

FAQ: Calculating Pressure and Temperature in a Container of Argon Gas

What is number density?

Number density, also known as particle density, is a measure of the number of particles per unit volume of a substance. It is typically expressed in units of particles per cubic meter (m-3).

How is number density related to Avogadro's number?

The number density of a substance is directly proportional to Avogadro's number, which is approximately 6.022 x 1023 particles per mole. This means that for a given volume of substance, the number of particles present will be higher for substances with smaller molecular weights.

What is the formula for calculating number density?

The formula for calculating number density is: number density = number of particles / volume of substance. This can also be written as n = N/V, where n is the number density, N is the number of particles, and V is the volume of the substance.

What is the relationship between number density and volume?

Number density and volume are inversely proportional. This means that as the volume of a substance increases, the number density decreases, and vice versa. This relationship is described by the formula n1 x V1 = n2 x V2, where n1 and V1 are the initial number density and volume, and n2 and V2 are the final number density and volume.

What is Vrms and how is it related to number density?

Vrms, or root mean square velocity, is a measure of the average speed of particles in a substance. It is related to number density through the ideal gas law, which states that the product of pressure and volume is proportional to the product of number density and Vrms squared. This relationship is described by the formula PV = 1/3 x n x m x Vrms2, where P is pressure, V is volume, n is number density, m is the mass of a single particle, and Vrms is the root mean square velocity.

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