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From: jbriggs444 on 18 Feb 2010 13:05
On Feb 18, 10:17 am, Uncle Al <Uncle...(a)hate.spam.net> wrote:
> Eeee wrote:
>
> > Please,
>
> > how to calculate the density of (saturated) moist air which include
> > condensed water.
>
> > Thanks in advance.
>
> Weight-averaged molecular weight, temperature, pressure.  Given the
> mass of 22.4 liters of gas, find the density.

You want molecular weight averaged by particle count, not mass.

Stop reading here if the error is already obvious to you.


A weight-averaged molecular weight would be computed as follows:

Suppose the atmosphere is 80% (by weight) Nitrogen and 20% Oxygen.
And let's stipulate a molecular weight of 28 for Nitrogen and 32 for
Oxygen.

So the weighted average has weight 0.80 on the 28 and 0.20 on the 32.
The weighted average is 28.8 grams per mole (exactly).

Now perform the [nonsensical] calculation that takes 22.4 liters = 1
mole of air and multiplies by the weight-averaged molecular weight of
28.8 to arrive at the supposed mass of 1 mole of air: 28.8 grams.

So let's split that mole back up. 28.8 grams. Of that mass, 5.76
grams (exactly) are Oxygen. And 23.04 grams (exactly) are Nitrogen.
That's the 80/20 ratio that we assumed at the outset.

So how many moles of Oxygen is that? 5.76/32 = 0.18
And how many moles of Nitrogen is that? 23.04/28 ~= 0.822857
How many moles total is that? ~1.002

So 1 mole = 1.002+ moles. It's magic!

[Of course it's not magic. It's just multiplying by the wrong
average]


The correct average is the one that's weighted by particle count.
28.7 grams per mole on the assumptions above. Not 28.8
From: Uncle Al on 18 Feb 2010 13:22
jbriggs444 wrote:
>
> On Feb 18, 10:17 am, Uncle Al <Uncle...(a)hate.spam.net> wrote:
> > Eeee wrote:
> >
> > > Please,
> >
> > > how to calculate the density of (saturated) moist air which include
> > > condensed water.
> >
> > > Thanks in advance.
> >
> > Weight-averaged molecular weight, temperature, pressure. Given the
> > mass of 22.4 liters of gas, find the density.
>
> You want molecular weight averaged by particle count, not mass.
>
> Stop reading here if the error is already obvious to you.
>
> A weight-averaged molecular weight would be computed as follows:
>
> Suppose the atmosphere is 80% (by weight) Nitrogen and 20% Oxygen.
> And let's stipulate a molecular weight of 28 for Nitrogen and 32 for
> Oxygen.
>
> So the weighted average has weight 0.80 on the 28 and 0.20 on the 32.
> The weighted average is 28.8 grams per mole (exactly).
>
> Now perform the [nonsensical] calculation that takes 22.4 liters = 1
> mole of air and multiplies by the weight-averaged molecular weight of
> 28.8 to arrive at the supposed mass of 1 mole of air: 28.8 grams.
>
> So let's split that mole back up. 28.8 grams. Of that mass, 5.76
> grams (exactly) are Oxygen. And 23.04 grams (exactly) are Nitrogen.
> That's the 80/20 ratio that we assumed at the outset.
>
> So how many moles of Oxygen is that? 5.76/32 = 0.18
> And how many moles of Nitrogen is that? 23.04/28 ~= 0.822857
> How many moles total is that? ~1.002
>
> So 1 mole = 1.002+ moles. It's magic!
>
> [Of course it's not magic. It's just multiplying by the wrong
> average]
>
> The correct average is the one that's weighted by particle count.
> 28.7 grams per mole on the assumptions above. Not 28.8

x%(MW1) + y%(MW2) + z%(MW)3...
x + y + z... = 100%

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm
From: jbriggs444 on 18 Feb 2010 15:46
On Feb 18, 1:22 pm, Uncle Al <Uncle...(a)hate.spam.net> wrote:
> jbriggs444 wrote:
>
> > On Feb 18, 10:17 am, Uncle Al <Uncle...(a)hate.spam.net> wrote:
> > > Eeee wrote:
>
> > > > Please,
>
> > > > how to calculate the density of (saturated) moist air which include
> > > > condensed water.
>
> > > > Thanks in advance.
>
> > > Weight-averaged molecular weight, temperature, pressure.  Given the
> > > mass of 22.4 liters of gas, find the density.
>
> > You want molecular weight averaged by particle count, not mass.
>
> > Stop reading here if the error is already obvious to you.
>
> > A weight-averaged molecular weight would be computed as follows:
>
> > Suppose the atmosphere is 80% (by weight) Nitrogen and 20% Oxygen.
> > And let's stipulate a molecular weight of 28 for Nitrogen and 32 for
> > Oxygen.
>
> > So the weighted average has weight 0.80 on the 28 and 0.20 on the 32.
> > The weighted average is 28.8 grams per mole (exactly).
>
> > Now perform the [nonsensical] calculation that takes 22.4 liters = 1
> > mole of air and multiplies by the weight-averaged molecular weight of
> > 28.8 to arrive at the supposed mass of 1 mole of air: 28.8 grams.
>
> > So let's split that mole back up.  28.8 grams.  Of that mass, 5.76
> > grams (exactly) are Oxygen.  And 23.04 grams (exactly) are Nitrogen.
> > That's the 80/20 ratio that we assumed at the outset.
>
> > So how many moles of Oxygen is that?  5.76/32 = 0.18
> > And how many moles of Nitrogen is that? 23.04/28 ~= 0.822857
> > How many moles total is that?  ~1.002
>
> > So 1 mole = 1.002+ moles.  It's magic!
>
> > [Of course it's not magic.  It's just multiplying by the wrong
> > average]
>
> > The correct average is the one that's weighted by particle count.
> > 28.7 grams per mole on the assumptions above.  Not 28.8
>
> x%(MW1) + y%(MW2) + z%(MW)3...
> x + y + z... = 100%
>

Is that an admission of error or a claim of correctness?

If you take a mole-weighted average molecular weight and multiply by
moles you get a mass in grams.

If you take a mass-weighted average molecular weight and multiply by
moles you get a number of no particular relevance expressed in units
of grams.
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