A 24 L welding tank contains of 285 bar of argon at 28 °C. Nitrogen is added to obtain an 80:20 argon:nitrogen mixture.
a) What are the partial pressures of argon and nitrogen? b) What will be the total tank pressure?
the Ar will effectively be "squeezed" into 80% of its previous volume
this will increase the tank pressure to 125% of the original
the pp of Ar is 80% of the total
the pp of nitrogen is 20%
To find total pressure since you have such a high pressure you have to treat the gases as non-ideal. this means that you have to find the pseudocritical temperature and pressure of the gas mixture which is
T'c= Ya(Tca)+Yb(Tcb)
and
P'c= Ya(Pca)+Yb(Pcb)
where Y is the mole fraction of the gas.
next you find the Pseudoreduced Temp and Pressure :
T'r= T/T'c
P'r=P/P'c
then look at a compressibility chart and find Zm- the compessibility factorof the gas mixture.
Next use equation V/n=Zm*R*T/P
and solve for P
This is called Kay's rule if you want to look it up in more detail.
I think it's important that you define what you mean by 80:20 mixture. Is that 80:20 by mass, by moles, or by volume?
To solve this problem, we need to use the Ideal Gas Law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.
First, let's calculate the number of moles of argon in the tank:
n_argon = (P_argon * V) / (R * T)
= (285 bar * 24 L) / (8.314 J/mol·K * (28 + 273.15) K)
We need to convert the temperature from Celsius to Kelvin by adding 273.15. Now, let's calculate the number of moles of nitrogen added to obtain an 80:20 argon:nitrogen mixture:
n_nitrogen = 0.2 * n_argon
a) Partial pressures:
The partial pressure of argon (P_argon) in the mixture is:
P_argon = (n_argon * R * T) / V
The partial pressure of nitrogen (P_nitrogen) in the mixture is:
P_nitrogen = (n_nitrogen * R * T) / V
b) Total tank pressure:
The total tank pressure is the sum of the partial pressures of argon and nitrogen:
Total pressure = P_argon + P_nitrogen
Now, let's substitute the values and solve the equations to get the answers.