Question

How many atoms of each element of $AgN{{O}_{3}}$ are in $0.15mol$ of $AgN{{O}_{3}}$ ?

Answer 1

Hint : A mole of substance is defined as the number of particles which is equal to $6.023\times {{10}^{23}}$ numbers of particles of that substance. A mole is used as a unit to specify the amount of a substance.

Complete Step By Step Answer:
According to the mole concept a mole of a substance contains that amount of substance which is equal to the molar mass of the substance. Thus we can say that one mole of carbon contains $12g$ of carbon which is the molar mass of carbon. Also one mole of water contains $18g$ of water which is the molar mass of water.
The term mole was given by a German chemist Wilhelm Ostwald in who describes that a large number of molecules is present in a mole of a compound. The number is $6.023\times {{10}^{23}}$ and called it as Avogadro’s number or constant denotes after the death of Amedeo Avogadro.
Mole is used as a unit of measurement to express the amount of a substance present in a specific weight of the substance. By definition a mole is equal to the amount of substance which is present in $6.023\times {{10}^{23}}$ number of particles. The particles considered may be atoms or molecules or ions.
Here, from $0.15$ mol of $AgN{{O}_{3}}$ we can find the moles of each element by counting how many of each element is present in the entire compound. In $AgN{{O}_{3}}$ there's one silver, one nitrogen and three oxygen. Then, we convert from moles of each element to the number of atoms using Avogadro's number $6.023\times {{10}^{23}}$
$A{{g}_{atoms}}=\left[ 0.15mol\left( AgN{{O}_{3}} \right) \right]\times \left[ \dfrac{1mol\left( Ag \right)}{1mol\left( AgN{{O}_{3}} \right)} \right]\times \left[ \dfrac{6.023\times {{10}^{23}}A{{g}_{atoms}}}{1mol(Ag)} \right]=9\times {{10}^{23}}A{{g}_{atoms}}$
${{N}_{atoms}}=\left[ 0.15mol\left( AgN{{O}_{3}} \right) \right]\times \left[ \dfrac{1mol\left( N \right)}{1mol\left( AgN{{O}_{3}} \right)} \right]\times \left[ \dfrac{6.023\times {{10}^{23}}{{N}_{atoms}}}{1mol(N)} \right]=9\times {{10}^{23}}{{N}_{atoms}}$
${{O}_{atoms}}=\left[ 0.15mol\left( AgN{{O}_{3}} \right) \right]\times \left[ \dfrac{3mol\left( O \right)}{1mol\left( AgN{{O}_{3}} \right)} \right]\times \left[ \dfrac{6.023\times {{10}^{23}}{{O}_{atoms}}}{1mol(O)} \right]=2.7\times {{10}^{23}}{{O}_{atoms}}$
Therefore, $9\times {{10}^{23}}A{{g}_{atoms}}$ , $9\times {{10}^{23}}{{N}_{atoms}}$ and $2.7\times {{10}^{23}}{{O}_{atoms}}$ atoms of each element of $AgN{{O}_{3}}$ are in $0.15mol$ of $AgN{{O}_{3}}$ .

Note :
The mole is used as the SI unit for describing the amount of a substance. The mole calculation is very useful for determining the exact amount of a substance. Using the number of moles we can determine the amount of the reactants and the amount of products produced from a chemical reaction.