How To Calculate Molar Mass From Pressure: Detailed Explanations


In this article, we learn about the how to calculate molar mass from pressure of gas molecules and how it can be calculated from pressure, volume, density, and detailed facts.

A molecule containing one mole of its own substance is called the molar mass of that particular substance. In simplification, it is the weight of one mole of a substance. By the help of Avogardo’s number we can calculate molar mass.

It is denoted by the formula,

M=m/n, Where m is the molar mass of a substance in gram, m is the mass of a substance in a gram ,n is the number of moles of a substance.

How to calculate molar mass from pressure ?

Using the ideal gas equation, we can easily calculate the molar mass from pressure.

It is evident from ideal gas equation

PV=nRT

P= pressure of a gas, V=volume of a gas, R=universal gas constant, T= temperature, n =number of moles of a gaseous molecule.

Again, we know

n =m/M = mass / Molar mass

so, putting the value of n in the above equation we get

PV=(m/M)RT

So, M = m(RT/PV)

M α 1/P [where α is the proportional constant]

So, we can say that from the above equation Molar mass is inversely proportional to the pressure of gaseous molecules. That means the higher the molar mass of gas the lower will be its pressure and vice versa, how to calculate molar mass from pressure is important factor.

how to calculate molar mass from pressure
Image credit Mathematics info

Calculate Molar mass from temperature

From the ideal gas equation, molar mass can be calculated from temperature.

PV=nRT

P= pressure of a gas, V=volume of a gas, R=universal gas constant, T= temperature, n =number of moles of a gaseous molecule.

Again, we know

n =m/M = mass / Molar mass

so, putting the value of n in the above equation we get,

PV=(m/M)RT

So, M = m(RT/PV)

M α T [where α is the proportional constant]

So, in the above relation, the relation between molar mass and temperature is directly proportional to each other. So, the higher the temperature higher will be the molar mass. how to calculate molar mass from pressure is important factor, here but we build relationship between molar mass and temperature here.

Calculate molar mass from Volume

Molar mass from Volume can be calculated by using the ideal gas equation

PV=nRT

P= pressure of a gas, V=volume of a gas, R=universal gas constant, T= temperature, n =number of moles of a gaseous molecule.

Again, we know

n =m/M = mass / Molar mass

so, putting the value of n in the above equation we get,

PV=(m/M)RT

So, M = m(RT/PV)

M α  1/V [where α is the proportional constant]

So, we can say that from the above equation Molar mass is inversely proportional to the volume of gaseous molecules. That means the higher the molar mass of gas the lower will be its volume and vice versa. how to calculate molar mass from pressure is important factor, here but we build relationship between molar mass and volume here.

Calculate molar mass from density

The density is equal to the mass of a substance over its volume.

Using the ideal gas equation, we can easily calculate the molar mass from density.

PV=nRT

P= pressure of a gas, V=volume of a gas, R=universal gas constant, T= temperature, n =number of moles of a gaseous molecule.

Again, we know

n =m/M = mass / Molar mass

so, putting the value of n in the above equation we get,

PV=(m/M)RT

M = (m/V)(RT/P)

M=ρ(RT/P)

So, M α ρ [where α is the proportional constant]

So, density is directly proportional to the Molar mass of a gaseous molecule. how to calculate molar mass from pressure is important factor. here but we build relationship between molar mass and density here.

Calculate molar mass from osmotic pressure

Using colligative property formula to calculate the molar mass from osmotic pressure.

From the colligative property,

Π=iCRT

Where Π is the osmotic pressure of a given substance, I = Vant Hoff factor (it is a constant), C= concentration of solute in a particular solution, R= Universal gas constant, and t = temperature.

For gaseous molecules, the concentration of solute in a particular solution will convert to molar mass and we omit the I factor as it is a constant term.

Now the equation becomes Π=MRT.

So Π α M [where α is the proportional constant]

So osmotic pressure is also directly proportional to the Molar mass of the gaseous molecule. how to calculate molar mass from pressure is important factor. here but we build relationship between molar mass and osmotic pressure here.

Calculate molar mass from Vapour pressure

From the colligative property, we know that relative lowering of vapor pressure is most suitable than vapor pressure.

So here we not only how calculate the molar mass from pressure but also calculate molar mass of a solute from relative lowering vapor pressure.

From Raoult’s Law

(P0-P)/P0 = X2……(i)

Where P0 is the vapor pressure of pure solvent and P is the vapor pressure of the solution. X2 is the mole fraction of solute.

Again, X2 = n2/(n1+n2)

For ideal solution n1>>>n2

So, the equation reduces to,

X2=n2/n1 ………(ii)

n2=W2/M2 and n1=W1/M1

then the equation (ii) becomes,

X2=(W2/M2)|(M1/W1)….(iii)

Comparing equations (i) and (iii) we get,

(W2/M2)(M1/W1)=(P0-P)/P0

M2= (W2/W1)M1 (P0/p0-p)

So, the Molar mass is directly proportional to the lowering vapor pressure of a volatile molecule. how to calculate molar mass from pressure is important factor. here but we build relationship between molar mass and vapour pressure here.

Frequently Asked question

How to calculate molar mass with ideal gas law?

By using the ideal gas law PV=nRT we can easily calculate the molar mass.

By using this law, we can calculate how to calculate molar mass from pressure , the relation between molar mass and pressure, molar mass and temperature, and molar mass and volume.

What is the basic difference between mole and molar mass?

Mole is defined as a number of substances per Avogadro’s number and molar mass is one mole of that substance.

Mole is defined as n=N/NA, Where NA is Avogadro’s number, and the value is 6.023*1023.

How many atoms are equal to one mole?

One mole is equal to 6.023*1023 atoms as it contains Avogadro’s number of atoms.

What is the unit of molar mass?

Molar mass = mass of the substance (in grams)/ number of moles

 So, the unit of molar mass is gram/mol.

Biswarup Chandra Dey

Chemistry is not all about reading line by line and memorize, it is a concept to understand in easy way and here I am share with you the concept about chemistry which I learn because knowledge is worth to share it.

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