Question

How many atoms are there in 75.9 g of sodium chloride (NaCl)?

Answer 1

`15.7\cdot 10^(23)`

Step-by-step explanation:

In order to solve this problem, we have to find the number of moles of NaCl first.

The number of moles of NaCl is given by:

`n=(m)/(M)`

where:

m = 75.9 g is the mass of the sample of NaCl in this problem

`M=58.4 g/mol` is the molar mass of NaCl, that is the amount of mass contained in 1 mole of the substance

Therefore, we have

`n=(75.9)/(58.4)=1.30 mol`

We also know that 1 mole of a substance contains always a number of molecules equal to the Avogadro number:

`N_A=6.022\cdot 10^(23)`

So, since here we have 1.30 moles, the number of molecules in this sample of NaCl is:

`N=nN_A=(1.30)(6.022\cdot 10^(23))=7.83\cdot 10^(23)`

However, here we are asked how many atoms the sample contains. Since 1 molecule of NaCl contains 2 atoms (1 atom of Na and 1 atom of Cl), it means that the number of atoms in this sample is twice the number of molecules, so:

`N' = 2N=2(7.83\cdot 10^(23))=15.7\cdot 10^(23)`