Question

Which of the following samples contain same number of molecules: (Atomic masses are :N = 14,

C = 12, O = 16, H = 1)

(A) 7gm N2 and 8gm NH3 (B) 9gm H2O and 2gm H2

(C) 22gm CO2 and 16gm O2 (D) All have same number of molecule​

Answer 1

Explanation:

Which of the following samples contain same number of molecules :

(A) 7 g N2 and 8 g NH3

(B) 9 g H2O and 2 g H2

(C) 22 g CO2 and 16 g O2 ✔

(D) All have same number of molecule

Option 1 :-

Molar mass of N2 is 14 × 2 = 28 g/mol

Molar mass of NH3 is 14 + 1 × 3 = 17 g/mol

As we know that :-

• mole = mass/GAM or GMM

GAM = Gram atomic mass

GMM = Gram molecular mass

Now,

In Case of N2

mole = 7/28 = 1/4 mole

and

In Case of NH3

mole = 17/17 = 1 mole

And

As we know that :-

• Number of molecules = mole × Avogadro's number

here we take Avogadro's number =

6 × 10²³ (approx)

Now,

In Case of N2 :-

number of molecules =

1/4 × 6 × 10²³

• » 1.5 × 10²³

And

In Case of NH3 :-

number of molecules =

1 × 6 × 10²³

• » 6 × 10²³

So,

Option 1 is incorrect.

Option 2 :-

Molar mass of H2O = 1×2 + 16 = 18 g/mol

Molar mass of H2 = 1 × 2 = 2 g/mol

As we know that :-

mole = mass/GAM or GMM

Now,

In Case of H2O

mole = 9/18 = 1/2 mole

And

In Case of H2

mole = 2/2 = 1 mole

And

As we know that :-

• Number of molecules = mole × Avogadro's number

here we take Avogadro's number =

= 6 × 10²³ (approx)

Now,

In Case of H2O :-

number of molecules =

1/2 × 6 × 10²³

• » 3 × 10²³

And

In Case of H2 :-

number of molecules =

1 × 6 × 10²³

• » 6 × 10²³

So,

Option 2 is incorrect

Option 3 :-

Molar mass of CO2 = 12 + 16×2 = 44 g/mol

Molar mass of O2 = 16×2 = 32 g/mol

As we know that :-

mole = mass/GAM or GMM

Now,

In Case of CO2 :-

mole = 22/44 = 1/2 mole

And

In Case of O2 :-

mole = 16/32 = 1/2 mole

And

As we know that :-

• Number of molecules = mole × Avogadro's number

here we take Avogadro's number =

6 × 10²³ (approx)

Now,

In Case of CO2 :-

number of molecules =

1/2 × 6 × 10²³

• » 3 × 10²³

And

In Case of O2 :-

number of molecules =

1/2 × 6 × 10²³

• » 3 × 10²³

So,

Option 4 is correct.

Note :-

Option 4 is correct because In Option 4 both samples contain same number of molecules.