Question

How many molecules of sulfur trioxide are in 78.00 grams?

Answer 1

To calculate the number of molecules first we have to calculate the number of moles of the given element as the number of moles is already given, then the mass can easily be calculated. A mole is generally used as a unit for the number of atoms or molecules or particles of a material.

Complete step by step solution:
The mole is a measurement or it is the basic unit which helps to calculate the amount of substance present in the given sample. 1 mole of a number is equal to Avogadro’s constant ${{N}_{A}}$.
Number of mol is calculated by ratio of given mass to the molar mass.
Number of mol of sulfur trioxide = $\dfrac{\text{given mass}}{\text{molar mass}}$
Given,
Given mass = 78 grams
Molar mass of sulfur trioxide = 80 g/mol
Number of moles =$\dfrac{78}{80}$
Number of molecules
$\implies \dfrac{78}{80}\times 6.022\times {{10}^{23}} \\\ \implies 5.871\times {{10}^{23}} \\\$

Hence, 5.871$\times {{10}^{23}}$ molecules of sulphur trioxide is present in 78.00 grams.

Note: 1 mole=$6.022X{{10}^{23}}$ particle or atoms or molecules or electrons or protons etc. The number of the constituent particles of atoms such as molecules or atoms or ions present in a given sample is related with the mass of the substance present in the sample using Avogadro's number. The SI unit of Avogadro’s number is inverse of mole i.e. $mol{{e}^{-1}}$
Avogadro’s number is dimensionless. It also helps to relate the molar volume of a substance to the average volume which is occupied by one of the particles.