Question

Calculate the number of molecules present in 0.5 moles of magnesium oxide $\left( {MgO} \right)$ .
(Atomic weights, $Mg = 24,O = 16$ )
A. $14.09 \times {10^{23}} $ molecules
B. $3.0115 \times {10^{23}} $ molecules
C. $30.12 \times {10^{23}} $ molecules
D. $14.09 \times {10^{23}} $ molecules

Answer 1

Hint: number of molecules is defined as the one mole of a substance that contains $6.023 \times {10^{23}}$ particles of the given substance. $6.023 \times {10^{23}}$ is also known as Avogadro’s number. With the help of Avogadro’s number we will find out the number of molecules present in magnesium oxide.

Complete step by step answer:
The molecular formula of magnesium oxide is $MgO$ .
Given data:
Atomic mass of magnesium $ = 24$
Atomic mass of oxygen $ = 16$
Now we will find the molecular mass of magnesium oxide:
$ \Rightarrow $Molecular mass of magnesium oxide $\left( {MgO} \right) = $ Atomic mass of magnesium $ + $ atomic mass of oxygen
$ \Rightarrow $ Molecular mass of magnesium oxide $\left( {MgO} \right) = 24 + 16$
$ \Rightarrow $ Molecular mass of magnesium oxide $\left( {MgO} \right) = 40$
Number of molecules is defined as the one mole of substance that contains $6.023 \times {10^{23}}$ particles of that substance.
In order to find the number of molecules present in magnesium oxide we will use Avogadro’s number.
Avogadro’s number $ = 6.023 \times {10^{23}}$ .
It is denoted by the symbol ${N_A}$ .
To convert moles to molecules then multiply it by Avogadro’s number.
It is given by the formula: number of particles $ = $ number of moles $ \times $ Avogadro’s number…1
Given: number of moles of magnesium oxide $ = 0.5moles$
To find: number of molecules present in $0.5moles$ of magnesium oxide $ = ?$
$6.023 \times {10^{23}} = 40g$ of magnesium oxide
$1mol$ contains $6.023 \times {10^{23}}$ molecules of magnesium oxide $\left( {MgO} \right)$ .
$\therefore 0.5mol$ will contain $ = ?$
Using the formula given in equation 1 we get,
number of particles $ = $ number of moles $ \times $ Avogadro’s number
substituting the values we get,
$ = \dfrac{{6.023 \times {{10}^{23}} \times 0.5}}{1}$
$ = 3.0115 \times {10^{23}}$molecules.
Therefore, number of molecules present in $0.5moles$ of magnesium oxide is $3.0115 \times {10^{23}}$

So the correct answer is option (B) $3.0115 \times {10^{23}}$.

Note: Avogadro’s number is a dimensionless quantity. The unit for Avogadro can be electrons, molecules, atoms depending upon the nature of the substance and sometimes the character of the reaction.