What is the molecular mass of the unknown gas in the atmosphere?

In summary, the task is to calculate the mass of an unknown gas molecule in the atmosphere given values for temperature, mass of the planet, radius, universal constant of gravitation, and pressure at two different altitudes. The relevant equation is g = kT/mλ, but there is no equation involving G. The attempt at a solution involved calculating g and using it to find m, but the calculated value does not match the values of the two possible gases.
  • #1
annalise17
10
0

Homework Statement



I need to calculate the mas of a molecule of an unknown gas in the atmosphere from the values:

T = 500 K
mass of the planet = 1.5 × 1024 kg
radius is 3.0 × 106 m
universal constant of gravitation, G = 6.67 × 10^−11 N m^2 kg^−2
P at ground level = 2.0 × 10^7 Pa
P at 50km altitude = 2.0 × 10^5 Pa

Homework Equations



g=kT/mλ

but I can't find an equation involving G :(

The Attempt at a Solution



I am completely stuck, if I can get ahint where to start I'll have a go and see if I get anywhere.
 
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  • #2
On Earth

F = mg = GmM/R^2 so g = GM/R^2
 
  • #3
Right, I've got so far as calculating g now and have calculated a very low value for g compared to Earth which is consistent with having a smaller mass than earth. I've also worked out an equation for m by rearranging λ=kT/mg ut the value doesn't match that of the two gases it could be by a factor of 10^3.
 
Last edited:

FAQ: What is the molecular mass of the unknown gas in the atmosphere?

What is molecular mass and why is it important?

Molecular mass, also known as molecular weight, is the sum of the atomic masses of all the atoms in a molecule. It is important because it helps determine the physical and chemical properties of a substance, such as boiling point, melting point, and reactivity.

How do you calculate molecular mass?

To calculate molecular mass, you need to know the atomic masses of all the elements in the molecule. Then, you multiply the atomic mass of each element by the number of atoms of that element in the molecule and add all the values together. This gives you the molecular mass in atomic mass units (amu).

What is the unit of measurement for molecular mass?

The unit of measurement for molecular mass is atomic mass units (amu) or daltons (Da). These units represent 1/12th of the mass of a carbon-12 atom.

Can molecular mass be negative?

No, molecular mass cannot be negative. It is a measure of the total mass of all the atoms in a molecule, and since atomic masses cannot be negative, molecular mass cannot be negative either.

How is molecular mass related to molar mass?

Molar mass is the mass of one mole of a substance, while molecular mass is the mass of a single molecule. They are related by Avogadro's number (6.022 x 10^23), which tells us the number of particles in one mole of a substance. To find the molar mass of a substance, you simply multiply the molecular mass by Avogadro's number.

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