Question

A gaseous mixture contains O2 and N2 in

the ratio 1 : 4 by weight. Then the ratio of

their number of molecules in the mixture is

(A) 3 : 32 (B) 7 : 32

(C) 1 : 4 (D) 3 : 16​

Answer 1

$\large \underline{\tt Given} :$

A gaseous mixture contains O₂ and N₂ in the ratio of 1 : 4 by weight.

$\large \underline{\tt To \: Find} :$

Ratio of number of molecules of O₂ and N₂ in the given mixture is

1. 3 : 32
2. 7 : 32
3. 1 : 4
4. 3 : 16

$\large \underline{\tt Answer} :$

$\pink{\bf 7 : 32}$ is the correct answer.

So, correct option is (B).

$\large \underline{\tt Solution} :$

As, we have a gaseous mixture contains O₂ and N₂ in the ratio of 1 : 4 by weight.

So, let weight of O₂ be "1x" and N₂ be "4x".

$\pink{\underline{\bf For \: O_2} : }$

We have :

• Weight of O₂ = 1x
• Mass of one mole in O₂ = 32 g
• Number of moles in O₂ = ?
• Number of molecules in O₂ = ?

We know that :

$\pink{\underline{\underline{\boxed{\bf Number \: of \: moles = \dfrac{Mass}{Mass \: of \: one \: mole}}}}}$

By substituting values :

$\sf : \implies Number \: of \: moles \: in \: O_2 = \dfrac{1x}{32}$

$\pink{\underline{\boxed{\bf Number \: of \: moles \: in \: O_2 = \dfrac{x}{32\: g}}}}$

Now, to find numbers of molecules, we have to multiply number of moles to Avogadro's number, which is 6.023 × 10²³.

$\pink{\underline{\underline{\boxed{\bf Number \: of \: molecules \: = Number \: of \: moles \: \times Avogadro's \: number}}}}$

By substituting values :

$\sf : \implies Number \: of \: molecules \: in \: O_2 = \dfrac{x}{32\: g} \times (6.023 \times 10^{23})$

$\pink{\underline{\boxed{\bf Number \: of \: molecules \: in \: O_2 = \dfrac{x}{32\: g} \times (6.023 \times 10^{23})}}}$

$\pink{\underline{\bf For \: N_2} : }$

We have :

• Weight of N₂ = 4x
• Mass of one mole in N₂ = 28 g
• Number of moles in N₂ = ?
• Number of molecules in N₂ = ?

We know that :

$\pink{\underline{\underline{\boxed{\bf Number \: of \: moles = \dfrac{Mass}{Mass \: of \: one \: mole}}}}}$

By substituting values :

$\sf : \implies Number \: of \: moles \: in \: N_2 = \dfrac{4x}{28}$

$\sf : \implies Number \: of \: moles \: in \: N_2 = \dfrac{1x}{7}$

$\pink{\underline{\boxed{\bf Number \: of \: moles \: in \: N_2 = \dfrac{x}{7\: g}}}}$

Now, to find numbers of molecules, we have to multiply number of moles to Avogadro's number, which is 6.023 × 10²³.

$\pink{\underline{\underline{\boxed{\bf Number \: of \: molecules \: = Number \: of \: moles \: \times Avogadro's \: number}}}}$

By substituting values :

$\sf : \implies Number \: of \: molecules \: in \: N_2 = \dfrac{x}{7\: g} \times (6.023 \times 10^{23})$

$\pink{\underline{\boxed{\bf Number \: of \: molecules \: in \: N_2 = \dfrac{x}{7\: g} \times (6.023 \times 10^{23})}}}$

$\pink{\underline{\bf For \: Ratio \: of \: Number \: of \: molecules} : }$

We have :

• Number of molecules in O₂ = $\sf \dfrac{x}{32\: g} \times (6.023 \times 10^{23})$
• Number of molecules in N₂ = $\sf \dfrac{x}{7\: g} \times (6.023 \times 10^{23})$

Now,

$\pink{\underline{\underline{\boxed{\bf Ratio \: of \: number \: of \: molecules \: in \: mixture = \dfrac{Number \: of \: molecules \: in \: O_2}{Number \: of \: molecules \: in \: N_2 }}}}}$

By substituting values :

$\sf : \implies Ratio = \dfrac{\dfrac{x}{32\: g} \times \cancel{(6.023 \times 10^{23})}}{\dfrac{x}{7\: g} \times \cancel{(6.023 \times 10^{23})}}$

$\sf : \implies Ratio = \dfrac{\dfrac{x}{32\: g}}{\dfrac{x}{7\: g}}$

$\sf : \implies Ratio = \dfrac{\cancel{x}}{32\: \cancel{g}} \times \dfrac{7 \: \cancel{g}}{\cancel{x}}$

$\sf : \implies Ratio = \dfrac{7}{32}$

$\pink{\underline{\underline{\boxed{\bf Ratio\: of \: number \: of \: molecules \: in \: mixture = 7 : 32}}}}$

$\underline{\sf Hence, \: Ratio \: of \: number \: of \: molecules \: in \: mixture\: is \: \pink{7 : 32}}$

Answer 2

Answer:

$\huge \boxed{ \red{7 : 32}} \: is \: the \: answer$

Explanation:

As given, the ratio of moles of O² or N² =

$\frac{1}{32} : \: \frac{4}{28} = \frac{1}{32} : \: \frac{1}{7} </p><p></p><p></p><p></p><p>$

$\large \boxed{ \red{(as \: we \: know, \: mole = \frac{w}{m})}}</p><p></p><p>$

The ratio of number of molecules =

$\frac{ \huge n \tiny a}{32}$

Answer 3

Answer:

$\huge \boxed{ \red{7 : 32}} \: is \: the \: answer$

Explanation:

As given, the ratio of moles of O² or N² =

$\frac{1}{32} : \: \frac{4}{28} = \frac{1}{32} : \: \frac{1}{7} </p><p></p><p></p><p></p><p>$

$\large \boxed{ \red{(as \: we \: know, \: mole = \frac{w}{m})}}</p><p></p><p>$

The ratio of number of molecules =

$\frac{ \huge n \tiny a}{32}$