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This is a Multiple Choice Questions as classified in NCERT Exemplar

Option (C), (D)

Molality: It is defined as the number of moles of solute divided by the mass of solvent in kg . It is denoted by m . The formula is expressed as

m = $\frac{\mathrm{n}}{\mathrm{W}\mathrm{}\mathrm{}}$

The SI unit of molality is 1 mol/kg

Molarity: It is defined as the number of moles of solute divided by the volume of solution in latice. It is represented by M  The formula of molarity is expressed as

M = $\frac{\mathrm{n}}{\mathrm{V}\mathrm{}\mathrm{}}$

Here, n is the number of moles of solute and V is the volume of solution expressed in liters. The SI unit of molarity is mol/ L .

Mole fraction (x ) : The mole fraction of a substance is defined as the number of moles of that substance divided by the total number of moles of all substances present in the solution.

Mass percent: it is defined as the weight of the solute divided by the total weight of the solution and the obtained result is multiplied by 100 in order to give a percent. Thus, mole fraction and mass percent are unitless.

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This is a Multiple Choice Questions as classified in NCERT Exemplar

Option(C), (D)

The number of moles is given by the following formula,

Moles = $\frac{\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{s}}{\mathrm{M}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$  ---------------(1)

The number of molecules can be calculated as, number of moles

= $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}}{\mathrm{A}\mathrm{v}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{}\mathrm{s}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}}$  ----------(2)

(C) The number of moles of N₂ is calculated by using equation (1) as follows,

Moles of N₂ = $\frac{14\mathrm{}\mathrm{g}}{28\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}}$  = 0.5 mol

The number of molecules can be calculated by using equation (2) as follows,

0.5 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}}$

number of molecules = 0.5 $*$  6.022 $*$  10²³

(D) The number of moles of H₂ is calculated by using equation (1) as follows,

Moles of H₂ = $\frac{1\mathrm{g}}{2\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}}$  = 0.5 mol

The number of molecules can be calculated by using equation (2) as follows,

0.5 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{e}\mathrm{s}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}}$

number of molecules = 0.5 $*$ 6.022 $*$  10²³

This is a Multiple Choice Questions as classified in NCERT Exemplar

Option(C), (D)

(A) The number of moles is given by the following formula,

Moles = $\frac{\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{s}}{\mathrm{M}\mathrm{o}\mathrm{l}\mathrm{a}\mathrm{r}\mathrm{}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}\mathrm{}$ -----------(1)

The number of moles of O₂ is calculated by using equation (1) as follows,

Moles of O₂ = $\frac{16\mathrm{}\mathrm{g}}{32\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$  = 0.5 mol

The number of atoms can be calculated as, number of moles

$\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{\mathrm{A}\mathrm{v}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{}\mathrm{s}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{}}\mathrm{}$ -----------(2)

On substituting the values in the equation (2)

0.5 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

number of atoms = 0.5 $*\mathrm{}$ 6.022 $*\mathrm{}$ 10²³

The number of moles of H₂ is calculated by using equation (1) as follows,

Moles of H₂ = $\frac{4\mathrm{g}}{2\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

= 2 mol

On substituting the values in the equation (2):

2 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

number of atoms = 2 $*\mathrm{}$ 6.022 $*\mathrm{}$ 10²³

(B) The number of moles of CO₂ is calculated by using equation (1) as follows

Moles of CO₂ = $\frac{44\mathrm{}\mathrm{g}}{44\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

= 1 mol

On substituting the values in the equation (2), the number of atoms can be calculated as ,

1 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

number of atoms = 1 $*\mathrm{}$ 6.022 $*\mathrm{}$ 10²³

(C) The number of moles of N₂ is calculated by using equation (1) as follows,

Moles of N₂ = $\frac{28\mathrm{g}}{28\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$  =1 mol

On substituting the values in the equation (2), the number of molecules can be calculated as

1 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

number of atoms = 1 $*\mathrm{}$ 6.022 $*\mathrm{}$ 10²³

The number of moles of O₂ is calculated by using equation (1) as follows,

Moles of O₂ = $\frac{32\mathrm{}\mathrm{g}}{32\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$  = 1

The number of atoms can be calculated as, number of moles

$\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{\mathrm{A}\mathrm{v}\mathrm{o}\mathrm{g}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{}\mathrm{s}\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{}}\mathrm{}$ -

On substituting the values in the equation (2)

1 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

number of atoms = 1 $*\mathrm{}$ 6.022 $*\mathrm{}$ 10²³

(D) The number of moles of C is calculated by using equation (1) as follows,

Moles of C = $\frac{12\mathrm{}\mathrm{g}\mathrm{}}{12\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}\mathrm{}}$ =1 mol

On substituting the values in the equation (2), the number of molecules can be calculated as

1 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

number of atoms = 1 $*\mathrm{}$ 6.022 $*\mathrm{}$ 10²³

The number of moles of Na is calculated by using equation (1) as fo

Moles of Na = $\frac{23\mathrm{}\mathrm{g}\mathrm{}}{23\mathrm{}\mathrm{g}\mathrm{}/\mathrm{}\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{}\mathrm{}}$ =1 mol

On substituting the values in the equation (2), the number of molecules can be calculated as

1 mol = $\frac{\mathrm{n}\mathrm{u}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}\mathrm{}}{6.022*\mathrm{}{10}^{23}\mathrm{}\mathrm{}\mathrm{}\mathrm{}}$

number of atoms = 1 $*\mathrm{}$ 6.022 $*\mathrm{}$ 10²³