# Molecular Weight Units for Mean Square Speed Calculation

• kd001
In summary, the mean square speed of molecules in an ideal gas can be calculated using the formula 3RT/M, where M is the molecular weight. The ideal units to use for R are m3 and Pa, which would result in M having units of kg/mol. However, if using L and atm as volume and pressure units, the units for M would be equivalent to 10.1325 Megagrams.
kd001
I need to calculate the mean square speed of molecules in an ideal gas. Mean square speed is equal to 3RT/M, where M is the molecular weight. But what units do I use for the molecular weight if I use 0.08206 L.atm/(mol.K) as R?

Thanks a lot.

The units for M would be something non-standard and awkward, if you are going to use L and atm as volume and pressure units. It would really be preferable to express R in m3 and Pa, then M can be in kg/mol.

That being said, if you are really curious about what the units would be, use the fact the volume is in liters and pressure is in atmospheres:

EDIT: see corrected version of the following, in next post

[STRIKE]1. Volume in liters implies that length units are ____?

2. And since pressure is in atm,[/STRIKE]
[STRIKE]1 atm = 1 m / d2

where "m" are the mass units you are looking for, and "d" is the length units found in step 1.[/STRIKE]​

[STRIKE]3. Solve that equation for "m", and then convert atm as necessary to get a value in kg.[/STRIKE]​

Last edited:
Ah, I hate it when people confuse mass and force, and I've done exactly that!

Okay, if you're interested in what funky units we get for mass, when we are using atm for pressure units and liters for volume, then read on:

1. Volume in liters implies that length units are ____?

2. And since pressure is in atm,
1 atm = 1 F / d2

where "F" is the force unit, and "d" is the length units found in step 1.​

3. Replace F with
F = m·d/t2
where "m" is the mass unit we are looking for, and "t" is the time unit. Let's assume we want to use seconds for the time units, so...

4. The equation from step 2 becomes
1 atm = (1 m·d/s2) / d2
1 atm = 1 m/(d·s2)​

5. Solve that equation for "m", and then convert atm as necessary to get a value in kg.​

It turns out that we get a mass unit equivalent to 10.1325 Megagrams. Not pretty.

Last edited:

## 1. What is the definition of molecular weight?

Molecular weight, also known as molar mass, is the mass of a molecule in atomic mass units (amu). It is calculated by adding the atomic mass of each atom in the molecule.

## 2. How is molecular weight used in calculating mean square speed?

Molecular weight is used in the calculation of mean square speed through the root-mean-square (RMS) equation, which is the square root of the average of the squared speeds of all particles in a system. This calculation helps determine the average speed of molecules in a gas or liquid.

## 3. What are the units for molecular weight?

Molecular weight is typically expressed in units of grams per mole (g/mol). This unit allows for easy conversion between the mass of a molecule and the number of moles present.

## 4. Can molecular weight units vary for different systems?

Yes, the units for molecular weight may vary depending on the system being studied. For example, in chemistry, the unit is often expressed as grams per mole, while in physics, it may be expressed in atomic mass units (amu). It is important to use the appropriate units for the specific system being analyzed.

## 5. How is molecular weight related to the kinetic energy of molecules?

Molecular weight is directly proportional to the kinetic energy of molecules. This means that as the molecular weight increases, the average speed of the molecules decreases, resulting in a lower kinetic energy. This relationship is important in understanding the behavior and properties of gases and liquids.

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