The molar volume is that the volume occupied by one mole of a substance which may be an element or a compound at degree Centigrade and Pressure (STP). In 1811, Avogadro explained that the volumes of all gases are often easily determined. Avogadro’s law states that equal volumes of all gases at an equivalent temperature and pressure contain equal numbers of particles. During this article, we’ll learn molar volume formula, perfect gas equation, and various numerical supported molar volume.
Molar Volume Formula
The Molar volume is directly proportional to molar mass and inversely proportional to density. The molar volume of a substance is its molar mass divided by its density. If the sample may be a mixture containing N components, we can approximate the molar volume because of the sum of the molar volume of its individual components, using the density of the mixture. However, many liquid-liquid mixtures, as an example, mixing pure ethanol and pure water, experience contraction or expansion upon mixing. This effect is “excess volume”.
Vm = relative atomic mass X (Molar mass / Density)
Where Vm is that the volume of the substance.
More accurate values of real gas molar volumes could also be obtained by using equations of state like the van der Waals equation developed in 1873, the Redlich-Kwong equation developed in 1949, the Soave-Redlich-Kwong equation developed in 1972 and therefore the Peng-Robinson equation developed in 1976.
Ideal Gas Equation
For ideal gases, the molar volume follows the perfect gas equation and this is often a decent approximation for several common gases at degree Centigrade and pressure. Rearrangement of the perfect gas equation can use to offer expression for the molar volume of a perfect gas:
Vm = V/n = RT/P
Hence, for a given temperature and pressure, the molar volume is that the same for all ideal gases and is understood to an equivalent precision because the gas constant: R = 0.082057338(47) L⋅atm⋅K−1⋅mol−1, that’s a relative standard uncertainty of 5.7×10−7, consistent with the 2014 CODATA recommended value. The molar volume of a perfect gas at 100 kPa (1 bar) is 0.022710980(38) m3/mol at 0 °C,0.024789598(42) m3/mol at 25 °C.
Solved Examples for Molar Volume Formula
Q 1] When sulfur burns in air it forms sulphur dioxide. What quantity of volume’s gas is produced when 1 g of sulfur burns? (ratio of Ar: S is 32) (We will measure all volumes at STP)
Step 1: Write a balanced equation for the reaction: S (s) + O2 (g) → SO2 (g)
Step 2: Get the amount of moles from the grams.
32 g of sulfur atoms = 1 mole of sulfur atoms
So, 1 g is equal to 1 ÷ 32 mole or 0.03125 moles of sulfur atoms
1 mole of sulfur atoms gives 1 mole of sulphur dioxide molecules
So, 0.03125 moles of sulfur atoms gives 0.03125 moles of sulphur dioxide
Step 3: Get the quantity.
1 mole of sulphur dioxide molecules features a volume of 22.4 at STP
So, 0,03125 moles features a volume of 0.03125 × 22.4 = 0.7 liters at STP
So, 0.7 litres of sulphur dioxide will be produced.
Q] Calculate the quantity of CO2 gas, CO2, occupied by 5 moles of the gas occupied at STP. Use Molar Volume Formula
Solution: Volume of CO2 = number of moles of CO2× 22.4 L
= 5 × 22.4
= 112 L