Question

Which of the following statements is/ are correct?
I $5$ moles of $C{O}_2$ and $5$ moles of $H_{2}O$ have the same mass.
II $100g$ of $N{H}_3$ has more atoms than that present in $100g$ of $N_2$.
III $16g$ of solid sulphur contains $3.76\times {10}^{22}$ molecules/

• A. I and II only
• B. II and III only
• C. III only
• D. I only

Answer 1

The correct option is C III only

Given,

$I⟶$ $5$ moles of $C{O}_2$ & $5$ moles of $H_{2}O$

Now Molar mass of $5$ moles of $C{O}_2$

$=5\times [12+32]g$

$=220g$

Molar mass of $5$ moles of $H_{2}O$

$=5[2+16]g$

$=90g$

$\therefore$ Molar mass of $5$ moles of $C{O}_2\ne 5$ moles of $H_{2}O$

$\therefore$ Statement $I$ is incorrect.

$II⟶$ No. of atoms in $100g$ $N{H}_3$

First, No. of moles of $100g$ $N{H}_3=\frac{100g}{17g/mol}$

$=5.88$ moles

We know $1$ mole of $N{H}_3$ has $6.023\times {10}^{23}$ atoms

$\Rightarrow 5.88$ mole $N{H}_3$ has $5.88\times 6.023\times {10}^{23}$ atoms

$=35.4\times {10}^{23}$ atoms

Also, No. of moles of $100g$ $N_2=\frac{100g}{28g/mol}=3.57$ moles

$\Rightarrow 3.57$ moles of $N_2$ has $3.57\times 6.023\times {10}^{23}$ atoms

$=21.5\times {10}^{23}$ atoms

$\therefore$ Statement $II$ is wrong.

$III⟶$ Solid sulphur molecule=$S_8$

Now, $1$ mole of $S_8$ molecule=$256g$

$\therefore 16g$ of solid sulphur=$\frac{16}{256}=0.0625$ moles

We know $1$ mole $S_8$ has $6.023\times {10}^{2}3$ molecules

$\Rightarrow 0.0625$ $S_8$ will have $0.0625\times 6.023\times {10}^{23}$

$=3.76\times {10}^{22}$ molecules

$\therefore$ Statement $III$ is correct.