9-Suggest the pressure and temperature at which 1.0 mol of (a) H2S, (b) CO2, (c) Ar will be in states that correspond to 1.0 mol N2 at 1.0 atm and 25°C.
Answers
To compare the corresponding states among different elements, the reduced pressure, temperature, of the elements must be same. The reduced temperature and pressure are defined as
Pr = Pm/Pc, Tr = Tm/Tc
Where,
Pr = Reduced pressure, Pc = Critical pressure
Tc = Critical temperature, Tr = Reduced temperature
Pm = Actual pressure, Tm = Actual temperature
We know,
The Critical pressure of Nitrogen = 33.55 atm
The Critical temperature of Nitrogen = 126.2K
The actual temperature of Nitrogen = 25 degree celcius = 298.12K
The actual pressure of Nitrogen = 1atm
a)Calculating the pressure and Temperature of Hydrogen sulfide
We know,
The Critical temperature of Hydrogen sulfide = 373.5K
The Critical pressure of Hydrogen sulfide = 89atm
Equating the reduced pressures and temperatures both the gases we have,
Pr for Nitrogen = Pr for Hydrogen sulfide
Pm/Pc = pm/Pc
1/33.55 = Pm/89
Pm = 1×89/33.55
=2.652atm
Tr for Nitrogen = Tr for Hydrogen sulfide
Tm/Tc = Tm/Tc
298.15/126.2 = Tm/373.5
Tm = 298.15×373.5/126.2
= 882.4K
b)Calculating the pressure and temperature for carbon dioxide
We know,
The Critical, temperature for Carbon dioxide = 304.25K
The Critical pressure for Carbon dioxide = 72.9atm
Equating the reduced pressure and temperature of both the gases we have,
Pr for Nitrogen = Pr for Carbon dioxide
Pm/Pc = Pm/Pc
1/33.55 = Pm/72.9
Pm = 1×72.9/33.55
= 2.173atm
Tr for Nitrogen = Tr for Carbon dioxide
Tm/Tc = Tm/Tc
298.15/126.2 = Tm/304.25
Tm = 298.15×304.25/126.2
= 718.8K
c)Calculating the pressure and temperature of Argon
We know,
The Critical temperature for Argon = 151.15K
The Critical pressure for Argon = 48.1atm
Equating the reduced pressures and temperatures of both the gases we have,
Pr for Nitrogen = Pr for Argon
Pm/Pc = Pm/Pc
1/33.55 = Pm/48.1
Pm = 1×48.1/33.55
= 1.433atm
Tr for Nitrogen = Tr for Argon
Tm/Tc = Tm/Tc
298.15/126.2 = Tm/151.15
Tm = 298.15×151.15/126.2
= 357.1K
a)Pressure = 2.652atm, Temperature = 882.4K
b)Pressure = 2.173atm, Temperature = 718.8K
c)Pressure = 1.433atm, Temperature = 357.1K
a)Pressure = 2.652atm, Temp = 882.4K
b)Pressure = 2.173atm, Temp = 718.8K
c)Pressure = 1.433atm, Temp = 357.1K
Explanation:
a)pressure and Temperature of Hydrogen sulfide;
Pr for Nitrogen = Pr for Hydrogen sulfide
Pm/Pc = pm/Pc
1/33.55 = Pm/89
Pm = 1×89/33.55
=2.652atm
Tr for Nitrogen = Tr for Hydrogen sulfide
Tm/Tc = Tm/Tc
298.15/126.2 = Tm/373.5
Tm = 298.15×373.5/126.2
= 882.4K
b)pressure and temperature for carbon dioxide:
Pr for Nitrogen = Pr for Carbon dioxide
Pm/Pc = Pm/Pc
1/33.55 = Pm/72.9
Pm = 1×72.9/33.55
= 2.173atm
Tr for Nitrogen = Tr for Carbon dioxide
Tm/Tc = Tm/Tc
298.15/126.2 = Tm/304.25
Tm = 298.15×304.25/126.2
= 718.8K
c)pressure and temperature of Argon:
Pressure for Nitrogen = Pressure for Argon
Pm/Pc = Pm/Pc
1/33.55 = Pm/48.1
Pm = 1×48.1/33.55
= 1.433atm
Tr for Nitrogen = Tr for Argon
Tm/Tc = Tm/Tc
298.15/126.2 = Tm/151.15
Tm = 298.15×151.15/126.2
= 357.1K