# Converting Density to Molecular Weight

#### Dragonrider99

Greetings all. I am currently in the midst of a Final Acceptance Testing for one of our customers that is purchasing some Density Meters. Physics is not my strong point as I am a Test Engineer and I desperately need some help. Our product is spec'd out such that it reports Density, Pressure, Current, and several other measurements but it does not report Molecular Weight. This customer is insisting on my telling him how to convert the Density Measurement to Molecular Weight and I am not sure. Basically the product is pressurized with Lab Grade Nitrogen and it detects Density via a change in frequency due to compression of a spool. Anyway, I found this formula for converting Molecular Weight to Density:

p=PM/RT where
p=Density
P=Pressure in Pascals
M=Molecular Weight
R=Universal Gas Constant
T=Temp in Kelvin

Re-arranging the formula I get:
M=pRT/P

My Values are:
p=8.65Kg.m3
P=786000 pascals
R=8.134j/mol*K
T=305.15 Kelvin

After doing the math I get 0.027Kg/mol

Is this correct or am I totally wrong?

Thanks

#### benit13

Caveat... I will accept no blame if something goes wrong!

Now that that's out of the way...

The only mistake seems to be your choice of value for the real gas constant; it's 8.314 J/(mol.kg)

Assuming an ideal gas:

$$\displaystyle PV = nRT$$

Since:

$$\displaystyle \rho = \frac{M}{V}$$

Substituting for V:

$$\displaystyle P\frac{M}{\rho} = nRT$$

$$\displaystyle \frac{M}{n} = \mu = \frac{\rho}{P}RT$$

$$\displaystyle \mu = \frac{8.65 * 8.314 * 305.15}{786000} = 0.02792$$ kg/mol = 27.92 g/mol

Carbon monoxide perhaps?

1. Make sure your real gas constant is correct (R = 8.314 J/(mol.K), not 8.134)
2. Make your customer aware that your measurement is a derived parameter using an equation that assumes an ideal gas.

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1 person

#### Woody

I am not sure what your customer is actually after.
The molecular weight is a constant which depends only on the material.
It is the weight (or more correctly Mass) of 1 Mole of the molecules of the material
(1 mole is a big number = about 6x10^23)

It allows one to estimate the number of molecules in a sample from its weight (mass) rather than by physically counting molecules (which is time consuming).

The standard atomic mass for Nitrogen is 0.014kg/mol
however you have Nitrogen gas, thus N2
giving molecular mass of 0.028kg/mol

I think that is fairly close to what you have calculated...

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#### Woody

What the customer wants.

Thinking about it, knowing the molecular mass of the gas being processed can tell you a fair amount about it.
For example your pure dry nitrogen gave a very close result to the book value.
However if it was contaminated (damp for example) the molecular mass would have been off.
Water with a molecular mass of 18grams/mole would raise the overall molecular mass of the mix.

Perhaps your customer wants to monitor a process to ensure that the (combined) molecular weights of the products remains within tolerable boundaries.

Benit's point about an ideal gas is pertinent.
Complex mixes, and complex molecules are less likely to match the theoretical "ideal" gas.
Have a look at the Wikipedia article linked here: <Ideal Gas>

If your customer wants to monitor a process (ensuring it does not change),
then relative accuracy might be more important than absolute accuracy.

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#### Dragonrider99

You guys are great! Thanks so much. Your comment about if there is another gas or substance in the mix hits home because otherwise I can't figure out for the life of me why they want that. Based on the data I have taken at various pressures and densities, the Molecular Weight always comes out to the "Book Value." If there IS another substance such as Water contaminating the gas, is there any way to determine the concentrations of each based on the calculated Molecular Weight based on the other measured parameters?

Not sure if I phrased that correctly but I hope you get the gist of what I mean. Otherwise thanks to all of you that have responded. I truly appreciate your help and inputs.

#### Woody

Contaminants

If you have a clear idea of what the molecular mass of the "clean" gas is
and a clear idea of what the contaminant might be, and what it's molecular mass is,
then you can start to get quantitative estimates of the level of contamination.

However if you just have an unknown contaminant, all you can get is a qualitative estimate of the level of contamination
(i.e. you don't know how much contaminant is there, but you do know if it gets better or worse).

#### donglebox

Referring to common practices,

If he needs a careful but easy-to-use quick-check manual, or reads out the transformation software tools according to the conditions,

You can sell this as an additional item.

After all, this has expanded the use of the device. It belongs to advanced tools.