Respuesta :
Ideal gas law :
PV= nRT
where,
P = pressure
V= volume
n= number of moles
R= universal gas constant
T = temperature
Now, number of moles = [tex]\frac{given mass in g}{molar mass}[/tex]
Put the value of number of moles in ideal gas law,
PV= [tex]\frac{given mass in g}{molar mass}[/tex]RT
PV= [tex]\frac{m}{M}[/tex]RT
PM= [tex]\frac{m}{V}[/tex]RT
Density is the ratio of mass to the volume, thus, above equation is also written as:
PM= [tex]\rho _{chlorine}[/tex]RT
[tex]\rho _{chlorine}= \frac{PM}{RT}[/tex]
Put the values,
Temperature = [tex]21^{o}C[/tex] + 273 = [tex]294 K[/tex]
Pressure = 0.8 atm
[tex]\rho _{chlorine}= \frac{0.8 atm\times 70 g/mol }{0.082057 L atm mol^{-1}K^{-1}\times 294^{o}C }[/tex]
= [tex]\frac{56 atm g/mol }{24.124758 L atm mol^{-1} }[/tex]
= [tex]2.32 g/L[/tex]
Now, specific gravity =[tex]\frac{\rho _{chlorine}}{\rho _{water}}[/tex]
=[tex]\frac{2.32 g/L}{1 g/cm^{3}}[/tex]
1 L = 1000 [tex]cm^{3}[/tex]
So, specific gravity =
[tex]\frac{2.32\times 10^{3} g/cm^{3}}{1 g/cm^{3}}[/tex]
= [tex]2.32 \times 10^{3}[/tex]
Thus, specific gravity is [tex]2.32 \times 10^{3}[/tex]
