Mole relations - Definitions, mathematical expressions, practice examples & FAQs

You must observe bananas can be purchased by number (dozen) and by the kilogram (weight) also curd is sold by weight as well as litre (volume), in the same way as sub atomic particle or material which is uncountable like atoms, molecules, ions, oils, detergent powder, sugar, salt, etc mole is the mathematical tool which makes relations between their number and weight or volume.

Table of contents

• Mathematical forms of mole
• Mole
• Normal temperature and pressure (NTP)
• Standard temperature and pressure (STP)
• Practice problems
• Frequently asked questions-FAQs

Mathematical forms of mole

1. $Mole=6.022\times {10}^{23} entities$

1 Mole=6.0221023 entities

We know, number of dozens =$\frac{number of entities}{12}$

Similarly, the number of moles = $\frac{number of entities}{6.022 \times {10}^{23}}$

2. Mole - weight relation

Number of moles = $\frac{weight of substance \left(g\right)}{Molar mass }$

The mass of $6.022\times {10}^{23}$ particles of any substance is termed the molar mass of the substance.

3. Mole-volume relationship

Number of moles = $\frac{volume of gas \left(L\right)}{Molar volume \left(L\right)}\left(at same T \& P\right)$

At STP,

The number of moles = $\frac{volume of gas \left(L\right)}{22.7 L }\left(at STP\right)$

Mole

We know one Dozen=12 entities

Entities can be a pen, pencil, etc, but entities can’t be atoms, ions, molecules, etc)

We know one $Mole=6.022\times {10}^{23} entities$

$6.022\times {10}^{23}$ number is known as Avogadro’s number and is represented by$N_A$.

$6.022\times {10}^{23}$ =1 $N_A$

We can say,

1 mole of H⁺ion = Collection of $6.022\times {10}^{23}{H}^{+}ion$

1 mole of H₂ molecules = Collection of $6.022\times {10}^{23}{H}_2 molecules$

1 mole of H atoms = Collection of $6.022\times {10}^{23}H atoms$

The quantity “mole” can be utilized for either a homogenous or heterogeneous mixture. The concept of mole can be utilized to solute or solvent depending upon one’s requirement.

A mole is defined as the amount of substance comprising the same number of fundamental entities as the number of atoms present in a pure sample of carbon weighing exactly 12 g or A mole is defined as the amount of a substance that contains exactly $6.022\times {10}^{23}$ elementary entities of the given substance.

Why did we take Avogadro's number to be $6.022\times {10}^{23}$

We know, the mass of one proton= $1.66\times {10}^{-24}g$

$\Rightarrow \frac{1}{1.66\times {10}^{-24}}\approx 6.022\times {10}^{23}$

1 amu= $1.66\times {10}^{-24}g$

Also remember: $1\mathit{ }\mathit{a}\mathit{m}\mathit{u}\times {\mathit{N}}_{\mathit{A}}\approx 1$

Normal temperature and pressure (NTP)

Temperature = ${20}^{0}C=293 K$

Pressure = 1 atm

It was experimentally observed that, at NTP conditions, one mole of an ideal gas occupies 24.0 L volume.

Standard temperature and pressure (STP)

Temperature =$0^{0}C=273 K$

Pressure = 1 atm

It was experimentally observed that, at STP conditions, one mole of an ideal gas occupies 22.7 L volume.

Video Link:

youtube.com/watch?v=OimGB-cQL9I

(Time stamp-17:20 till the end)

Practice problems

Q1. Find the total number of Helium (He) atoms present in 2.5 moles of Helium.

(N_A refers to Avagadro’s number)

a. N_A
b. 2N_A
c. 2.5N_A
d. 3N_A

Answer: (C)

Solution: we know 1 mole = $6.022\times {10}^{23}$ entities

The total number of He atoms = 2.5$\times$ $6.022\times {10}^{23}$ = 2.5N_A

Q2. Find the total mass in grams of 2.5 moles of iron.(Molar mass of Fe = 56 g mol^-1)

A. 140 g
B. 150 g
C. 56 gg
D. 156 g

Answer: (A)

Solution: number of moles = $\frac{weight of substance \left(g\right)}{Molar mass }$

$Weight of iron= number of moles \times Molar mass$

Weight of iron = (2.5 $\times$56) g = 140 g

Q 3. Find the volume at STP for 160 g SO₃ gas.

A. 44.8 L
B. 45.4 L
C. 11.2 L
D. 5.6 L

Answer: (B)

Solution: number of moles of SO₃ = $\frac{weight of substance \left(g\right)}{Molar mass }=\frac{160}{80}=2 mol$

number of moles =$\frac{volume of gas \left(L\right)}{22.7 L }\left(at NTP\right)$

Volume of SO₃ gas = 1 mol$\times$ $22.7 L=45.4 L$

Q4. Find the charge of 56 mg of Fe³⁺ ions.

A. 144.56 C
B. 72.30 C
C. 96.35 C
D. 192.7 C

Answer: (C)

Solution: number of moles of Fe³⁺ = $\frac{weight of substance \left(g\right)}{Molar mass }=\frac{0.056}{56}=$ $1 \times {10}^{-3} mol$

The total number of Fe³⁺ ions = $1 \times {10}^{-3}\times 6.022\times {10}^{23}=6.022 \times {10}^{20}$

One ion Fe³⁺ contains three positive charges.

We know the magnitude of the charge of one proton equals the magnitude of the charge of one electron.

Charge of one proton = $1.6\times {10}^{-19}C$

Total charge on Fe³⁺= $1.6\times {10}^{-19}C\times 6.022 \times {10}^{20}=96.35 C$

Frequently asked questions (FAQs)

Q1. Why do we use mole fraction?
Answer: The mole fraction is the ratio of the number of single component molecules (or moles) to the total number of molecules in the mixture (or moles). The mole fraction is important when two reactive components are combined together because the ratio of the two components may be understood if the mole fraction of each component is known.

Q2. Is partial pressure equal to mole fraction?
Answer: Each gas's partial pressure in a mixture is proportional to its mole fraction. The pressure exerted by each gas in the gas mixture (its partial pressure) is independent of the pressure exerted by all other gases in the mixture.

Q3. What is the significance of the mole concept?
Answer: The mole definition pervades all aspects of chemistry. Because most quantitative chemical calculations are based on the mole, knowledge of the mole is essential for chemistry students. Understanding how the mole relates to mass, the number of individuals, and so on.

Q4. What do the terms gram-atom and gram-molecule mean?
Answer: Moles are the units of measurement for gram-atoms and gram-molecules in current usage.

E.g- 1 gram-atom Na⁺ = 1 mol of Na⁺

1 gram-molecule H₂O = 1 mol of H₂O

Q5. When is Mole Day celebrated?

Answer: $1N_A=6.022\times {10}^{23}$

Mole Day is celebrated on September 23, from 6 AM to 6 PM.