There are 8.43x10²¹ total atoms in 0.280 g of P₂O₅.
Explanation:
Let's follow some steps to calculate the total atoms.
1st) Calculate the molar mass of P₂O₅
Look for the atomic weight of each atom in the Periodic table:
- Atomic weight of Phosphorus = 31 g/mol
- Atomic weight of Oxygen = 16 g/mol
Then, multiply each atomic weight by its coefficient to calculate the molar mass of P₂O₅:
(Atomic weight of P .2) + (Atomic weight of O .5)= Molar mass of P₂O₅
(31 g/mol.2) + (16 g/mol.5) = 62 g/mol + 80 g/mol = 142 g/mol
2nd) Calculate the moles of P₂O₅ that are contained in 0.280 g
This step is easy using a Rule of three thinking that if 142 g of P₂O₅ represents a mol of P₂O₅ the 0.280 g will be "x" moles:
142 g 1 mol of P₂O₅
0.280 g x = (0.280 g.1 mol)/142 g =0.002 mol of P₂O₅
This means that 0.002 moles of P₂O₅ weights 0.280g.
3rd) Calculate the moles of P and O
To see clear how many moles of each atoms are in the molecule of P₂O₅ we disassociate it:
P₂O₅ → 2P + 5O
From the reaction we know that 1 mol of P₂O₅ produces 2 moles of phosphorus and 5 moles of oxygen. Now we can make a relation and thinking that if 1 mol of P₂O₅ produces 2 moles of P the 0.002 moles of P₂O₅ that we have will produce "x" moles of P:
1 mol of P₂O₅ 2 moles of P
0.002 mol of P₂O₅ x = (0.002 mol.2moles)/1mol = 0.004 moles of P
We use the same reasoning for oxygen:
1 mol of P₂O₅ 5 moles of O
0.002 mol of P₂O₅ x = (0.002 mol.5moles)/1mol = 0.01 moles of O
Up to here we have 0.004 moles of atoms of phosphorus and 0.01 moles of atoms of oxygen.
4th) Calculate the total atoms
To this step it is important to remember that 1 mol of something representa a quantity of 6.022x10²³ (that is called Avogadro's number) So, 1 mol of atoms represents 6.022x10²³ atoms.
Now, if we know that in 1 mol of phosphorus atoms is equal to 6.022x10²³ atoms of phosphorus the 0.004 moles that we have will be equal to "x" atoms:
1 mol of P 6.022x10²³ atoms of P
0.004 mol of P x = (0.004 . 6.022x10²³)/ 1 = 2.41x10²¹ atoms of P
Use the same reasoning for oxygen:
1 mol of O 6.022x10²³ atoms of O
0.01 mol of O x = (0.01 . 6.022x10²³)/ 1 = 6.022x10²¹ atoms of O
Now that we have the number of atoms of phosphorus and oxygen let's sum them to find the total atoms:
2.41x10²¹ atoms of P + 6.022x10²¹ atoms of O = 8.43x10²¹ total atoms
Finally, there are 8.43x10²¹ total atoms (of phosphorus and oxygen) in 0.280 g of P₂O₅.
