# A mass of 135 g of an element is known to contain 30.1 \times 10^{23} atoms. What is the element?

## Question:

A mass of 135 g of an element is known to contain {eq}30.1 \times 10^{23} {/eq} atoms. What is the element?

## Molar mass

Molar mass is a property of any substance. It is defined as the quotient of the mass and the amount of substance in a given sample,

Usually, the molar mass is given in g{eq}\cdot {/eq}mol{eq}^{-1} {/eq}. One mol equals {eq}6.02\times 10^{23} {/eq} particles of a given type, atoms, molecules, etc.

The number {eq}N_A=6.02\times 10^{23} {/eq} is called the Avogadro constant.

We are given the number {eq}N=30.1 \times 10^{23} {/eq} of atoms in the bulk of {eq}135 {/eq} g. From the definition of the amount of substance the bulk contains,

{eq}n=\dfrac{N}{N_A}=\dfrac{30.1 \times 10^{23}}{6.02 \times 10^{23}}=5 {/eq} mol.

Knowing the amount of substance we can obtain the molar mass of the substance from equation (1),

{eq}\mu=\dfrac{135}{5}=27 {/eq} g{eq}\cdot {/eq}mol{eq}^{-1} {/eq}.

The molar mass is an intrinsic property of the substance, hence it can serve as a unique identifier. Searching the chemical tables we can readily check that this molar mass corresponds to aluminum,

{eq}\mu_{Al}=27 {/eq} g{eq}\cdot {/eq}mol{eq}^{-1} {/eq}. 