Question

(a) mass of 0.5 mole of ${N_2}$ gas (Atomic mass of ${N_2}$= 14u)
(b) number of particles in 46 g of Sodium atoms (Atomic number of Na = 23u)
(c) the number of moles for in 52 g of He (Atomic mass of He = 4u)

Answer 1

In the given three calculations, the number of moles is needed to be calculated. The number of moles of an atom is calculated by dividing the weight of the atom with the atomic weight of the atom.

Complete answer:
(a) Given,
Moles of ${N_2}$ is 0.5 mole.
Atomic mass of ${N_2}$ is 14 u.
The formula for calculating moles of compounds is shown below.
$n = \dfrac{m}{A}$
Where,
n is the moles of compound.
m is the mass of the compound.
A is the atomic weight.
To calculate the mass of ${N_2}$, the formula of moles is rearranged as shown below.
$m = n \times A$
To calculate the mass of ${N_2}$, substitute the values of moles and atomic weight in the above equation.
$\Rightarrow m = 0.5 \times 14$
$\Rightarrow m = 7g$
Therefore, the mass of ${N_2}$ is 7g.
(b) Given,
Mass of the sodium atom is 46 g.
Atomic number of Na is 23 u.
The formula for calculating moles of compounds is shown below.
$n = \dfrac{m}{A}$
Where,
n is the moles of compound.
m is the mass of the compound.
A is the atomic weight.
To calculate the moles of an atom, substitute the value of mass and atomic weight in the above equation.
$\Rightarrow n = \dfrac{{46g}}{{23g/mol}}$
$\Rightarrow n = 2mol$
1 mole of Na atom contains $6.022 \times {10^{23}}atoms$
Thus, 2 mole of Na atoms contains $2 \times 6.022 \times {10^{23}}$= $1.2044\times {{10}^{24}}$ atoms.
Therefore, the number of particles in 46 g of Sodium atoms is $1.2044 \times {10^{24}}$.
(c) Given,
Mass of He is 52 g.
Atomic weight of He is 4u.
The formula for calculating moles of compounds is shown below.
$n = \dfrac{m}{A}$
Where,
n is the moles of compound.
m is the mass of the compound.
A is the atomic weight.
To calculate the moles of He atom, substitute the value of mass and atomic weight in the above equation.
$\Rightarrow n = \dfrac{{52g}}{{4g/mol}}$
$\Rightarrow n = 13mol$
Therefore, the number of moles of He is 13 mol.

Note: When the moles of any molecule is calculated then the mass of the molecule is divided by the molecular weight which is the sum of the atomic weight of the individual atom.