Gram Atomic Mass: Atomic Mass, Molecular Mass, Molar Mass, Gram Atomic Mass, Gram Molecular Mass, Practice Problems & FAQs

Raushni, a student of class 11th went to a grocery store and asked for 2kg of sugar. The shopkeeper placed a 2kg weight on one side of the manual weighing scale and on the other side he started adding sugar till the weighing scale reached its equilibrium.

undefined

On her way back home Raushni came up with a question:

Is this exactly 2kg?

Well, if you look at the back side of weights, there is an authorized signature of the government. These weights have been calibrated according to the standard weight system. Hence, you can assure that the pulses are exactly 2kg.

A standard weighing system and a universally accepted unit are required to define any quantity. So numerous methods were established to define the mass of an atom such as molar mass, molecular mass, atomic mass, gram atomic mass & gram molecular mass.

In this concept page, we will understand the concept of gram atomic mass and how it came into inception!

TABLE OF CONTENT

Atomic mass
Molecular mass
Mole Concept
Molar mass
Gram Atomic mass (G.A.M)
Gram molecular mass (G.M.M)
Practice problems
Frequently asked question - FAQs

Atomic mass:

Atomic mass is defined as the amount of matter that makes up an element's atom. In other words, one atom's mass, measured in amu or u.

$M a s s o f o n e a t o m = M a s s o f t o t a l p r o t o n + m a s s o f t o t a l n e u t r o n + m a s s o f t o t a l e l e c t r o n$

For the sake of numerical simplicity, we ignore the mass of the electron when calculating atomic mass (the mass of one atom) and assume that the mass of one proton is equivalent to one neutron's mass.

We can say, $M a s s o f a p r o t o n = m a s s o f a n e u t r o n = m a s s o f a n u c l e o n$

$M a s s o f o n e a t o m = M a s s o f t o t a l p r o t o n s + m a s s o f t o t a l n e u t r o n s = m a s s o f t o t a l n u c l e o n s$

$M a s s o f o n e a t o m = t o t a l n u m b e r o f n u c l e o n s \times m a s s o f o n e n u c l e o n$

(Total nucleons are equal to the sum of neutrons and protons.)

$M a s s o f o n e a t o m = t o t a l n u m b e r o f n u c l e o n s \times 1.66 \times 10^{- 24} g$

$M a s s o f o n e a t o m = t o t a l n u m b e r o f n u c l e o n s \times a m u$

$M a s s o f o n e a t o m = R e l a t i v e a t o m i c m a s s \times a m u$

$A t o m i c m a s s = R e l a t i v e a t o m i c m a s s \times a m u$

Example: Calculate the atomic mass of Na23 atom

Solution: number of proton = 11

Number of neutron = 23- 11= 12

Total number of nucleons = 23

Atomic mass of Na atom = 23 amu

Molecular mass:

Mass of a given molecule of a compound is referred to as molecular mass. In other words it can be also defined as the sum of the mass of all the atoms comprising the respective molecule is the molecular mass of the given molecule. It is generally measured in ‘amu’.

Example. Calculate the molecular mass of methane(CH4)

Solution:

Molecular mass of $C H_{4} = (4 \times a t o m i c m a s s o f H a t o m) + (1 \times a t o m i c m a s s o f C a t o m)$

$= (4 \times 1 a m u) + (1 \times 12 a m u) = 16 a m u$

Molecule	Molecular mass
N₂	28 amu
NH₃	17 amu
NaOH	40 amu

Mole Concept:

The amount of substance that contains the same number of fundamental components as the number of atoms present in a pure sample of carbon weighing exactly 12 g is known as a mole. A mole is the volume of a substance that contains exactly 6.0221023 of its elementary constituents.

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

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

$6.022 \times 10^{23}$ = 1 NA

Mole to number of entities

Mole to mass

Mole to Volume

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

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

Number of moles = weight of substance (g)Molar mass

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

Number of moles = volume of gas (L)Molar volume (L) (at same T & P)

At STP,

The number of moles = volume of gas (L)22.4 L (at STP)

Molar mass:

A substance's molar mass is its mass in grams per mole of the compound.

For elements or molecules, the molar mass is displayed. The molar mass is simply the element's mass expressed in atomic mass units in the case of single elements or individual atoms. In other words, the atomic mass and molar mass of an atom are identical. Molar mass can be used to determine a particle's identity because it is equal to atomic mass for individual atoms. C, for instance, has an atomic mass of 12. Since carbon only contains one atom and is therefore found to be monatomic, its molar mass is also 12.

The mass of 6.0221023 entities of any particles are considered as the molar mass of that particular substance.

Molar mass is the weight of a single mole of an individual molecule, as opposed to molecular mass, which is the weight of a single molecule.

The molar mass of C atom = mass of $6.022 \times 10^{23}$ C atom

Molar mass of NH₃ molecule = mass of $6.022 \times 10^{23}$ NH₃ atom

Molar mass of SO42- ion = mass of $6.022 \times 10^{23}$ SO42- ions

Example:

Let's say someone has a mole of sodium hydroxide. The individual would contain 6.0221023 sodium hydroxide molecules in that mole of sodium hydroxide, based on Avogadro's number.

1 mol NaOH = $6.022 \times 10^{23}$ NaOH molecules

Sodium hydroxide molecule dissociates to give :

$N a O H_{(a q)} \to {N a}^{+}_{(a q)} + O {H^{-}}_{(a q)}$

One mole of sodium hydroxide produces one mole of sodium ions and one mole of hydroxide ions in accordance with the dissociation described above. Consequently, we can also state that one mole of sodium hydroxide yields 6.0221023 of sodium ions and hydroxide ions.

Thus,

$1 m o l N a O H = 6.022 \times 10^{23} N a O H m o l e c u l e s$

$1 m o l N a O H = 6.022 \times 10^{23} O H^{-} i o n s$

$1 m o l N a O H = 6.022 \times 10^{23} N a^{+} i o n s$

Gram Atomic mass (G.A.M):

The mass of one mole of an element's atoms is known as the gram atomic mass of that element. Although it has its unit in grammes, it is numerically equivalent to the value of the element's atomic mass unit. For instance, let’s calculate the gram atomic mass of nitrogen. It’s atomic mass is 14 amu.

From mole concept, we came to know that

Number of moles of a substance $= \frac{G i v e n m a s s}{A t o m i c m a s s}$

In case of nitrogen,

Atomic mass = 14 amu

1 mole of nitrogen $= \frac{G i v e n m a s s o f n i t r o g e n}{A t o m i c m a s s o f n i t r o g e n}$

$1 = \frac{G i v e n m a s s o f n i t r o g e n}{14 a m u}$

Hence, the given mass of nitrogen = 14 g and this is the gram atomic mass of nitrogen.

In other words, Atomic mass of an atom expressed in grams is called gram atomic mass or simply we can say, the mass of 6.0221023 atoms (Avogadro's Number) is the gram atomic mass.

Example. Calculate the gram atomic mass of B10 atom.

Solution: In case of boron,

Atomic mass = 10 amu

1 mole of boron $= \frac{G i v e n m a s s o f b o r o n}{A t o m i c m a s s o f b o r o n}$

$1 = \frac{G i v e n m a s s o f b o r o n}{10 a m u}$

Hence, the given mass of nitrogen = 10 g and this is the gram atomic mass of boron.

Note:

Element	Relative Atomic Mass	Atomic mass	Gram atomic mass
N	14	14 amu	14 g
C	12	12 amu	12 g
H	1	1 amu	1 g
Ne	20	20 amu	20 g
O	16	16 amu	16 g
Na	23	23 amu	23 g

Gram molecular mass (G.M.M):

A substance's molecular weight or the total of all the atomic masses in its molecular formula is equivalent to one gramme of molecular mass. It is equivalent to a molecule's molecular mass in grams. Mass of 1 molecule expressed in grams or mass of 6.0221023 molecules.

Example. . Calculate gram molecular mass of water (H2O)

Solution:

Molecular mass of H2O= (2 atomic mass of H atom) + (1 atomic mass of O atom)

= (2 1 amu) + (1 16 amu) = 18 amu

Gram molecular mass of H2O= (2 GAM of H atom) + (1 GAM of O atom)

= (2 1 g) + (1 16 g) = 18 g

Molecule	Gram Molecular mass
CO2	44 g
KOH	56 g
NaCl	58.5 g

Practice problems:

Q 1. Which of the following represents the gram molecular mass of CO₂.

44 g
18 g
4.4 g
56 g

Answer: (A)

Solution: Molecular mass of CO₂= (1 atomic mass of C atom) + (2 atomic mass of O atom)

$= (1 \times 12 a m u) + (2 \times 16 a m u) = 44 a m u$

Gram molecular mass of CO₂= (1 GAM of C atom) + (2 GAM of O atom)

$= (1 \times 1 2 g) + (2 \times 16 g) = 44 g$

Q 2. Calculate the gram atomic mass of Mg.

14 g
24 g
44 g
34 g

Answer: (B)

Solution: In case of Magnesium,

Atomic mass = 24 amu

1 mole of Magnesium $= \frac{G i v e n m a s s o f M a g n e s i u m}{A t o m i c m a s s o f M a g n e s i u m}$

$1 = \frac{G i v e n m a s s o f M a g n e s i u m}{24 a m u}$

Hence, the given mass of Magnesium= 24 g and this is the gram atomic mass of Magnesium.

Q 3. Find the total mass in grams of 6 moles of Na ? (Molar mass of Na= 23 g mol-1)

138 g
158 g
238 g
13.8 g

Answer: (A)

Solution: number of moles = $\frac{w e i g h t o f s u b s t a n c e (g)}{M o l a r m a s s}$

$W e i g h t o f s u b s t a n c e = n u m b e r o f m o l e s \times M o l a r m a s s$

$W e i g h t o f s u b s t a n c e = (6 \times 23) g = 138 g$

Q 4. Which of the following is the correct unit gram atomic mass?

g/litre
g/mol
g
None of the above

Answer: (C)

The mass of one mole of an element's atoms is known as the gram atomic mass of that element. Gram atomic mass is measured in grams. Hence, option C is the correct choice.

Frequently asked question-FAQs:

1. Can any element's relative atomic mass be fractional?
Answer: Because it is just the total number of protons and neutrons, relative atomic mass cannot ever be expressed as a fraction. There are never any fractions of protons or neutrons.

2. Is it possible to define relative atomic mass in relation to elements other than carbon?
Answer: Yes, relative atomic mass is defined mathematically in relation to any other element, but in the scientific community, carbon is regarded as the standard.

Standard definition; Relative atomic mass = $\frac{M a s s o f o n e a t o m o f a n y e l e m e n t}{\frac{1}{12} \times m a s s o f o n e C^{12} a t o m}$

In respect of oxygen; Relative atomic mass = $\frac{M a s s o f o n e a t o m o f a n y e l e m e n t}{\frac{1}{16} \times m a s s o f o n e O^{16} a t o m}$

3. Why is the mass of Chlorine written in fraction?
Answer: Cl35.5 written because of its isotopes, Cl present in nature in different isotopes in different natural abundance (%). So, due to their isotopes, they have fractional mass. We can call it weighted average atomic mass.

4. What distinguishes atomic mass from atomic weight?
Answer: Atomic weight is typically the weighted average of isotopic abundance in nature as opposed to atomic mass, which is typically used for single isotopes. Because it is correlated with the number of protons and neutrons in the nucleus, atomic mass is always a whole number.