## Desity Formula and Measurement

**Density formula** of gas, liquid, and solid molecules is the measurement of mass or weight per unit volume of material at a given temp and pressure. Standard or normal **density calculator** uses for calculating densities at 0°C and one atm pressure. Calculation of the density of the gas measured by the ratio of molar masses of equal volumes of gas and oxygen and molar mass of oxygen taken 16. The ideal gas equation uses to calculate molecular weight and density of ideal gases but this equation approximately obeyed under normal conditions. Therefore, the molar mass measurement by ideal gas law, not an accurate one.

### Limiting Density of Gases Formula

The ideal gas equation for n moles gases

PV = nRT

or, P = (g/V)RT

ρ = **density measurement** of the gas, M = mass (gm) per unit volume (cc), called normal density formula per unit pressure. Therefore, the molar mass of the gas can be experimentally determined by using this expression. Such **density calculation** from the above gas equation measured only an approximate and not an accurate one in chemical and physical science. But the above equation accurately obeyed at very low pressure at P→0. So the molar mass value of this pressure gives accurate and the equation represented as,

M = (ρ/P)_{P→0} ×RT

This (ρ/P)_{P→0} = limiting the density of a gas.

But direct use of this relation poses some difficulty since, at P→0, ρ→0 and not possible to determine experimentally. Therefore, the above graphical measurement has taken advantage to calculate molar mass by density.

Generally, the value of the molar mass of gas measured from the density comparison with oxygen at the same temperature. For example, ρ of CH_{3}F = 1.5177 while for oxygen = 1.4177. Thus, M_{CH3F} = M_{O2} × (1.5177/1.4177) = 32 gm/mole, this is the correct molar mass of CH_{3}F.

### Abnormal Vapour Density Calculator

Vapour density of a substance defined as the ratio of the density of gaseous state of the substance and hydrogen under the same temp and pressure. It is the quantity having no unit or dimensions and reprinted as, D_{0} = M_{0}/2, where M_{0} = formula molecular weight of the gasses.

But for many chemical substances, like ammonium chloride, phosphorus pentachloride, nitrogen peroxide, etc has calculated vapour densities less than the theoretical measurement. Only at a high temp D_{0}≈D_{0}/2. This phenomenon is called abnormal vapour density. The cause of this phenomenon due to the thermal dissociation of the above chemical substances.

NH_{4}Cl → NH_{3} + HCl

PCl_{5} → PCl_{3} + Cl2

N_{2}O_{4} → 2NO_{2}

I_{2} → 2I

### Formula for Calculating Abnormal Density

At constant pressure due to dissociation, the volume of the gases increases with the increase of the mole number. Since mass remains the same and D_{0} decreases. The extent or fraction of the total number of molecules that suffer dissociation calculate the degree of dissociation. Let us take one molecule of substance A splits up into n molecules of B by heat,

A → nB

At equilibrium for each gm mole of A will be (1 – α) gm moles of undissociated A and nα gm moles of B. So the total number of gm mole of gas present = (1-α) + nα or 1 + (n-1)α. When V = volume occupied per unit volume of gas or vapour and D_{0} denotes the density measurement absence of any dissociation. If D denotes the observed densities when actual dissociation occurred and the total weight of the gas = W.

W = D_{0}V and W = D×V[1 + (n-1)α]

∴ D_{0}/D = 1 + (n-1)α

This expression shows that, at high temperature, α = 1(complete dissociation) and for NH_{4}Cl, and PCl_{5}, n=2, thus D = D_{0}/2, and this density formula also saw in the experimental calculator.