Question

How many atoms of cadmium, Cd, are in 3.00 g of cadmium?

Answer 1

Hint: Generally we know that 1 mole of any substance (described as molecular weight in grams) is equal to the value $6.022 \times {10^{23}}$. So to calculate the number of atoms, first we need to find the number of moles present in the cadmium atom.

Complete step by step answer:
Given,
The mass of cadmium is 3.00 g.
From the periodic table, we can know the atomic weight of the cadmium which is 112.414g/mol.
To calculate the number of atoms present in 3.00 g of cadmium, first calculate the number of moles of cadmium atom as the mass of the cadmium atom and the atomic weight is given.
The number of moles is calculated by dividing the mass with the atomic weight of the atom.
The atomic weight is obtained by the average sum of the isotope of the atom each multiplied by their natural abundance.
The formula to calculate the number of moles is shown below.
$n = \dfrac{m}{A}$
Where,
n is the number of moles
m is the mass
A is the atomic weight
To calculate the moles of cadmium, substitute the values in the above equation.
$\Rightarrow n = \dfrac{{3.00g}}{{112.414}}$
$\Rightarrow n = 0.0266$mol
We know that 1 mole of any substance contains $6.022 \times {10^{23}}$ atoms where the value is known as the Avagadro’s number and the constant is said as Avagadro’s constant.
So, the number of atoms is calculated as shown below.
$\Rightarrow 0.0266 \times 6.022 \times {10^{23}}$
$\Rightarrow 1.60 \times {10^{22}}$

Therefore, the number of cadmium atoms present in 3.00 gram of cadmium is $1.60 \times {10^{22}}$ atoms.

Note: Don’t get confused by the formula of moles as normally to calculate the moles, the mass is divided by the molecular weight. As in this question for cadmium atom is asked not for the compound so atomic weight is used instead of molecular weight.