Question

What is the mass of ${{4.10}^{21}}$ platinum atoms?

Answer 1

Hint: Mass of an atom is the mass of all the particles present in it. The particles are Avogadro numbers, which are $6.022\times {{10}^{23}}$atoms. These atoms make 1 mole of any compound or element. This means 1 mole of any compound has this much number of atoms, which is equal to the molar mass of that element of the compound.

Complete answer:
We have been given a ${{4.10}^{21}}$ number of platinum atoms whose mass is to be determined. This determination will require the mole concept. As we know, 1 mole of any element or compound has the mass equal to molecular mass which contains the atoms equal to Avogadro number that is $6.022\times {{10}^{23}}$ atoms.
First we will calculate the number of moles in${{4.10}^{21}}$platinum atoms, and then through the number of moles and molar mass of platinum, we will determine the mass of these atoms.
Number of moles in ${{4.10}^{21}}$platinum atoms = $\dfrac{1\,mole}{6.022\times {{10}^{23}}atoms}\times {{4.10}^{21}}atoms$
Number of moles in ${{4.10}^{21}}$ platinum atoms = 0.0066 moles
Now, as we know number of moles = $\dfrac{mass}{molar\,mass}$ ,
Therefore, the mass = number of moles$\times $molar mass of platinum.
Mass = 0.0066 moles$\times $195 g/mol
Mass = 1.28$\simeq $1 g
Hence, the mass of ${{4.10}^{21}}$platinum atoms is 1 gram.

Note:
The mass of an atom is the sum of the number of protons and the neutrons present in that atom. These are also called nucleons as they are present in the nucleus. Platinum contains 78 protons and 117 neutrons that make its molar mass as 195 g/mol. This means that each 1 mole of platinum has 195 gram atomic weight.