Determining relative density

How to calculate relative density

Water density is often used for calculating relative density [Wikimedia]

Den­si­ty is a phys­i­cal val­ue equal to the ra­tio of the mass of a sub­stance to its vol­ume. This val­ue is mea­sured in g/cm³ [kg/m³].

ρ = m/V.

Of­ten in de­ter­min­ing den­si­ties of aque­ous so­lu­tions for stan­dard den­si­ty, the den­si­ty of pure wa­ter is used, which un­der nor­mal con­di­tions is ap­prox­i­mate­ly equal to 1 g/cm³. For con­ve­nient cal­cu­la­tion, the rel­a­tive den­si­ty of a sub­stance is of­ten used.


Rel­a­tive den­si­ty

Rel­a­tive den­si­ty is a val­ue de­ter­mined as the ra­tio of the den­si­ty of the sub­stance stud­ied to the den­si­ty of a sub­stance cho­sen as the “stan­dard” in this case. Rel­a­tive den­si­ty is a non-di­men­sion­al val­ue, as in de­ter­min­ing it one val­ue of den­si­ty is di­vid­ed by an­oth­er. Not only the change in the nu­mer­i­cal val­ue of the pa­ram­e­ter is tak­en into ac­count, but also the change of its di­men­sion – if the di­men­sion is di­vid­ed by it­self it is com­plete­ly re­duced:

d = P/P₀ (den­si­ty of giv­en sub­stance – Р, den­si­ty of stan­dard sub­stance – Р₀).

Con­di­tions may be in­di­cat­ed af­ter d. For ex­am­ple, d²⁰₄ in­di­cates that den­si­ty was cal­cu­lat­ed at 20 ᵒC (68 ᵒF), and that the den­si­ty of wa­ter at 4 ᵒC (39.2 ᵒF) was tak­en as the stan­dard.

Click here for mak­ing in­ter­est­ing ex­per­i­ments with wa­ter.

In the case of wa­ter, fun­da­men­tal dif­fer­ences can­not usu­al­ly be seen be­tween the den­si­ty of the sub­stance and its rel­a­tive den­si­ty, as the den­si­ty of wa­ter is round­ed to 1. The pres­ence or ab­sence of a di­men­sion of val­ue helps us to de­ter­mine pre­cise­ly which val­ue is de­ter­mined – rel­a­tive or not.


Some­times the rel­a­tive den­si­ty is also de­ter­mined for gas­es ac­cord­ing to a sim­i­lar prin­ci­ple:

Dₐᵢᵣ= Mᵣ(gas)/Mᵣ ₐᵢᵣ (den­si­ty of gas by air is de­ter­mined as a ra­tio of the rel­a­tive molec­u­lar mass of gas to the rel­a­tive­ly molec­u­lar mass of air, which is al­ways equal to 29). In­stead of air, any oth­er gas can be used as a stan­dard.

What can in­flu­ence the val­ue of den­si­ty

The val­ue of rel­a­tive, as well as or­di­nary, den­si­ty, is not a con­stant val­ue even for the same sub­stances. De­pend­ing on the tem­per­a­ture of the en­vi­ron­ment, the val­ue may be­come high­er or low­er (the de­pen­dence of the den­si­ty of the nec­es­sary sub­stance from at­mo­spher­ic con­di­tion may be found from ref­er­ence ta­bles or de­ter­mined by de­vices in a se­ries of ex­per­i­ments with dif­fer­ent con­di­tions).

For ex­am­ple, at 20 ᵒC (68 ᵒF), the den­si­ty of dis­tilled wa­ter is 998.203 kg/m³, while at 4 ᵒC (39.2 ᵒF) it is 999.973 re­spec­tive­ly. With a pre­cise de­ter­mi­na­tion of rel­a­tive den­si­ty, these dif­fer­ences may in­flu­ence the fi­nal re­sult.

Pycnometer [Wikimedia]

How to mea­sure rel­a­tive den­si­ty

Rel­a­tive den­si­ty at the same tem­per­a­ture can be mea­sured with a py­c­nome­ter – it is first weighed emp­ty, then with the stan­dard sub­stance (for ex­am­ple dis­til­late) and then with the sub­stance un­der in­ves­ti­ga­tion. In some cas­es, to de­ter­mine rel­a­tive den­si­ty an aerom­e­ter is used, but the pre­ci­sion of re­sults is low­er.

Ex­am­ples of cal­cu­la­tions

If the den­si­ties of two sub­stances are giv­en in solv­ing a prob­lem, to find the rel­a­tive den­si­ty, the def­i­nite den­si­ty sim­ply needs to be di­vid­ed by the stan­dard. For ex­am­ple, if the den­si­ty of a hy­drochlo­ric acid so­lu­tion is 1.150 kg/m³, and the stan­dard den­si­ty of sul­fu­ric acid is around 1.800 kg/m³, then the den­si­ty of hy­drochlo­ric acid di­vid­ed by sul­fu­ric acid is:

Sulfuric acid 3D structure [Wikimedia]

d = P/P₀ = 1150/1800 = 0.64.

With gas­es, molec­u­lar mass is used. So the den­si­ty of chlo­rine Cl₂ di­vid­ed by air is:

Dₐᵢᵣ= Mᵣ(Cl₂)/Mᵣ ₐᵢᵣ = 71/29 = 2.45.

Chlorine [Wikimedia]

Cal­cu­la­tions of rel­a­tive den­si­ty are of­ten used in prac­tice for sim­pli­fied es­ti­ma­tions.