Question

Calculate the number of
particles in each of the
following :-


(i) 46 g of Na atoms
(number from mass)

(ii) 8 g 0² molecules (number of
molecules from mass )

iii) 0.1 mole ov Carbon atoms (number from given moles)
​

Answer 1

in 46 gram of sodium number of atoms are 2NA

or 12 x 10²³ atoms

in 8 g oxygen there are 1.5 x 10²³ molecules

point 1 mole of carbon atom has 6 x 10²² atoms

hope it helps

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Answer 2

The Avogadro constant 6.022 × 10²³ is defined as the number of atoms in exactly 12g of carbon- 12 atom.

(i)46 g of Na atoms (number from mass)

$\implies \pmb{ \bm{\sf\dfrac{Given \: Mass}{Molar \: Mass} \times Avogadro \: number}}$

$\implies \sf N = \sf\dfrac{m}{M} \times N_0$

$\implies \sf N = \sf \cancel\dfrac{46}{23} ^{ ^{ \normalsize 2} } \times 6.022 \times {10}^{23} \: \: \: \: \: \: \: \: \: \: \because \left\lbrack M = \dfrac{ Given \: Mass}{ 2} \right \rbrack$

$\implies \sf N = 2 \times 6.022 \times {10}^{23}$

$\implies \sf N = 12.044 \times {10}^{23}$

$\rule{200pt}5pt$

(ii)8 g $\sf 0_{2}$ molecules (number of molecules from mass)

$\implies \pmb{ \bm{\sf\dfrac{Given \: Mass}{Molar \: Mass} \times Avogadro \: number}}$

$\implies \sf N = \sf\dfrac{m}{M} \times N_0$

As we know that atomic mass of Oxygen = 16 u

$\sf \therefore Molar \: mass \: of \: O_2 \: Molecules = 16 \times 2 = 32g$

$\implies \sf N = \sf \cancel\dfrac{8}{32} ^{ ^{ \normalsize \frac{1}{4} } } \times 6.022 \times {10}^{23}$

$\implies \sf N = \dfrac{1}{4} \times 6.022 \times {10}^{23}$

$\implies \sf N = 0.25 \times 6.022 \times {10}^{23}$

$\implies \sf N = 1.5055 \times {10}^{23}$

$\implies \sf N \simeq 1.51 \times {10}^{23}$

$\rule{200pt}5pt$

(iii) 0.1 mole ov Carbon atoms (number from given moles)

$\implies \pmb{ \sf No. \: of \: moles = \dfrac{No. \: of \: particles}{Avogadro \: Number}}$

$\implies \sf No. \: of \: particles = Avogadro \: Number \times No. \: of \: moles$

$\implies \sf N = \sf n\times N_0$

$\implies \sf N = 0.1 \times 6.022 \times {10}^{23}$

$\implies \sf N = \dfrac{1}{10} \times 6.022 \times {10}^{23}$

$\implies \sf N = 0.6022 \times {10}^{23}$

$\implies \sf N = 0.6022 \times 10 \times {10}^{22}$

$\implies \sf N = 6.022 \times {10}^{22}$

$\underline{ \rule{300pt}8pt}$

Additional informations:-

Molecular mass :

The molecular mass of a substance is the sum of the atomic masses of all the atoms in a molecule of the substance. It is therefore the relative mass of a molecule expressed in automic mass units (u).

Valency :

It is defined as the combining capacity of an atom of an element acquire noble gas configuration. It is equal to the number of electrons lost, gained of shared during the formation of a chemical compound.

Atomic size :

The distance from the centre of the nucleus to the outermost shell of an atom is called the atomic radius of that atom.