Ideal Gas problem! help please! is this correct?

Question

Hello I want to know if I did the following question correctly :

A neon sign is made of glass tubing whose inside diameter is 0.025m and whose length is 5.5 m. If the sign contains neon at presure 0.00234 atm at 308 K, how many grams of neon are in the sign.

v = (pi)r^2 = 0.011m^3 = 1.1 x 10^-5 L

n = PV/RT = 0.00234 * 1.1 x 10^-5 / 0.08206 * 308 K

= 1.02 x 10^-9 mol

mass = moles * Mr =1.02 x 10^-9 mol * 20.18 = 2.06 x 10^-8 g

Then the another question asks :

If the pressure exerted by ozone, O3, in the stratosphere is 3.0 x 10^-3 atm and the temperature is 250 K, how many ozone molecules are in a liter?

Could somebody please show me how to do it as I know that I am doing it wrong as i obtain 4.8 x 10-5 molecules

THANK YOU!!

Answer 1

For the first part . Volume of tube =pir^2l =3.142*0.0125*0.0125*5.5 = 0.0027 cubic metres.

PV=nRT so guess you will have to go through that part of the calculation again

Ref to answer below 0.025 is diameter so r =1/2 diameter 0.0125. length = 5.5m not 5m.

Answer 2

First question V = 5m*pi*(0.025m)^2 = 0.0098 m^3 everything else is ok.

Second question: Assuming O3 is in thermal equillibrium you still use

PV = nRT --> solve for n ---> n = PV/(RT)

Since there are 6.02x10^23 molecules per mole (Na - Avagodro's number), number of O3 molecules is

N = nNa = Na * PV/(RT) = 8.8x10^19 molecules/liter