What is the formula for calculating the mass of air in a piston?

[Gregs6799]

Homework Statement

Homework Equations

pV = (m/Mr)RT (this is the formula given but I got the wrong answer using it)

The Attempt at a Solution

Mass = PV / RT
R = 8.314
P1 x V2 / R x T1
M = 220 x 0.1 / 8.314 x 298 = 788.549kg
Mass = 788.549kg

P = 440000
V = 0.1
R = 8.314
T = 298
440000 x 0.1 = 44000
M = mRT / PV
M = 44000 x 8.314 x 298 / 440000 x 0.1 = 24.77g.
Mass of air in piston = 24.77g.
P1 = 440000

V2 = 0.1
R = 8.314
T = 25 + 273 = 298 (from Celsius to kelvin)
P1 x V2 / R x T1
M = 440000 x 0.1 = 44,000
8.314 x 298 = 2477.572
44000 / 2477.572 = 17.759kg

All the above values are correct but the formulas and answers are incorrect.
I've posted here before and your probably sick and tired of trying to help me out but if anyone can give me the correct formula for question b only a is correct just b, I'd be very appreciative, but just the formula, try not to go too in depth with any replies as it will go over my head and confuse me all I need is the formula and in what order do the values need to go in, he answer should be in kgs.

Thank you.[/B]

 

[TSny]

Homework Equations

pV = (m/Mr)RT (this is the formula given but I got the wrong answer using it)

Hello.
Note the Mr in the formula. Did you include that in your calculation for part (b)?
You would be able to catch such errors if you included units when doing the calculation.

 

[Gregs6799]

I think Mr = 44000 / 17.75 = 2478 and probably didn't put in the formula, not sure what units that would be in.

 

[Chestermiller]

I think Mr = 44000 / 17.75 = 2478 and probably didn't put in the formula, not sure what units that would be in.

When you are sure of the correct units, please let us know. We will be waiting.

 

[Gregs6799]

I tried replacing (m/Mr) with n (moles) nRT
17.75 x 8.314 x 298 = 43976 (unless that's in grams is way too high.)
And RT / PMr
8.314 x 298 / 44000 x 2478 = 139.53, again too high if its in kgs.

 

[Chestermiller]

$$moles=\frac{PV}{RT}=\frac{(220000)(0.2)}{(8.314)(298)}=\frac{(440000)(0.1)}{(8.314)(298)}=17.76\ moles$$Molecular weight of air = 29 gm/mole. So, $$mass=(17.76)(29)=515\ grams=0.515\ kg$$

 

[Gregs6799]

So I wasn't far off the right answer with
440000 x 0.1 = 44,000
8.314 x 298 = 2477.572
44000 / 2477.572 = 17.759 moles
just didn't multiply by 29, which I didn't see in the given formula, unbelievable.

Sorry for taking up much of your time, your either born with the brains or your not.
Many thanks.