Specific Gravity or Relative Density

Definition:

Specific gravity or Relative Density of a substance is the ration of the density of that substance to the density of a reference substance. We can calculate the specific gravity of liquid and gas assuming the reference substance as water and air respectively.

1.     Specific gravity of Liquid

Specific gravity of liquid is defined as the ratio of density of the liquid at a standard or any temperature to the density of water at some standard reference temperature at atmospheric pressure. We take water as reference as the specific gravity of water [(S.G)water] is 1.

Mathematically,

Specific Gravity of liquid = (S.G)liquid = (density of liquid at any temperature) / (Density of water at some standard temperature)

For scientific purpose the distilled water is taken as reference.
For industrial purpose the normal water is taken as reference.

Standard reference temperature = 4°C
Atmospheric pressure = 760 mm of Hg

As per American Petroleum Institute (API), Standard reference temperature = 15.6°C or 60°F

As per International standard Organization (ISO), standard reference temperature = 15°C or 59°F

2.     Specific Gravity of Gas

The specific gravity of gas can be defined in either of two ways.

(i)                  Real Specific Gravity: The ratio of the density of the gas (ρgas ) to the density of air (ρair ) at a particular temperature and pressure is called the Real Specific Gravity.

Mathematically,
(S.G)gas = (ρgas / ρair) T,P

(ii)           Ideal Specific Gravity: Ratio of the molecular weight of the gas (Wgas) to the                                  molecular weight of air (Wair), is called the Ideal Specific Gravity.

Mathematically,
(S.G)gas = (Wgas / Wair)

◘ At normal atmosphere, temperature and pressure, the real specific gravity [(RSG)gas] and the Ideal Specific Gravity [(ISG)gas] of Gas are same, except- Steam, Carbon di oxide and some gases.

PROOF:

Ideal Gas Law = PV=nRT

P= pressure
V= volume
n= number of moles
R= Gas constant=8.314
T= temperature

For Real Gas = PV=nZRT

Z is defined as the ratio of the volume of the gas to the volume occupied by the same number of moles of ideal gas, at particular temperature and pressure.

Z = (Volume of real gas) / (Volume of same no. of moles of ideal gas)
Z is called the Compressibility factor.

PV=nZRT
PV = [m/Mw] ZRT
m/V = (PMW)/(ZRT)
ρ = (PMW)/(ZRT)
ρgas = [P (MW)gas]/ (ZgasRT)…………….(I)
ρair = [P (MW)air]/ (ZairRT)……………….(II)

Now,

(RSG)gas = ρgas / ρair

Putting the values of (I) and (II) in this equation,

(RSG)gas = [(MW)gas/(MW)air] * [ Zair/Zgas]

(RSG)gas = (ISG)gas * [Zair/Zgas]……………….(III)

At normal atmosphere, temperature and pressure,

Zair = Zgas

From equation (III),

(RSG)gas = (ISG)gas

Hence proved.

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