Gram Molecular Mass: Gram Atomic Mass, Gram Molecular Mass, Practice Problems and FAQs

Rupali, a student of class 11th went to a fruit market and asked for 3kg apples. The vendor placed a 3kg weight on one side of the manual weighing scale and on the other side he started adding apples till the weighing scale reached its equilibrium.

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

Is this exactly 3kg?

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 apples are exactly 3kg.

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 molecular mass and how it came into inception.

Table of contents

Gram Molecular Mass (G.M.M)
Gram Atomic mass (G.A.M)
Practice problems
Frequently asked question - FAQs

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 acetic acid(CH3COOH)

Solution:

Molecular mass of CH3COOH= (4 atomic mass of H atom) + (2 atomic mass of O atom) + (2 atomic mass of C atom)

$= (4 \times 1 a m u) + (2 \times 16 a m u) + (2 \times 12 a m u) = 60 a m u$

Gram molecular mass of CH3COOH= (4 GAM of H atom) + (2 GAM of O atom) + (2 GAM of C atom)

$= (4 \times 1 g) + (2 \times 16 g) + (2 \times 12 g) = 60 g$

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

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 fluorine,

Atomic mass = 19 amu

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

$1 = \frac{G i v e n m a s s o f f l u o r i n e}{19 a m u}$

Hence, the given mass of fluorine = 19 g and this is the gram atomic mass of fluorine.

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 Fe56 atom.

Solution: In case of iron,

Atomic mass = 56 amu

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

$1 = \frac{G i v e n m a s s o f i r o n}{56 a m u}$

Hence, the given mass of iron = 56 g and this is the gram atomic mass of iron.

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

Practice problems:

Q 1. Which of the following represents the gram molecular mass of NO2?

46 g
18 g
4.4 g
56 g

Answer: (A)

Solution: Molecular mass of $N O_{2} = (1 \times a t o m i c m a s s o f N a t o m) + (2 \times a t o m i c m a s s o f O a t o m)$

$= (1 \times 14 a m u) + (2 \times 16 a m u) = 46 a m u$

Gram molecular mass of $N O_{2} = (1 \times G A M o f N a t o m) + (2 \times G A M o f O a t o m)$

$= (1 \times 1 4 g) + (2 \times 16 g) = 46 g$

Q 2. Calculate the atomic mass of Ca?

30 g
40 g
50 g
34 g

Answer: (B)

Solution: In case of Calcium,

Atomic mass = 40 amu

1 mole of Calcium $= \frac{G i v e n m a s s o f C a l c i u m}{A t o m i c m a s s o f C a l c i u m}$

$1 = \frac{G i v e n m a s s o f C a l c i u m}{40 a m u}$

Hence, the given mass of Calcium = 40 g and this is the gram atomic mass of Calcium.

Q 3. Find the total mass in grams of 3 moles of O .(Molar mass of O= 16 g mol-1).

48 g
58 g
4.8 g
13.8 g

Answer: (A)

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

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

$W e i g h t o f s u b s t a n c e = (3 \times 16) g = 48 g$

Hence, option A is the correct choice.

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

g/litre
g/mol
g
None of the above

Answer: (C)

Solution:

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. Does molecular mass correspond the same with gram molecular weight?
Answer: The molecular mass of a substance expressed in grams (in amu) is known as the gramme molecular mass, or it can also be thought of as the mass in grams that is numerically equal to the molecular mass. Even though their numerical values are identical, they differ in units. Molecular mass is expressed in amu whereas gram molecular mass is expressed in g.

2. What is the relationship between amu and gram?
Answer: $1 a m u = \frac{1}{12} \times m a s s o f o n e C^{12} a t o m$

Atomic mass unit (amu) is equal 112 of the mass of one atom of C12 isotope.

$1 a m u = \frac{1}{12} \times 12 \times m a s s o f o n e n e u t r o n = m a s s o f 1 n e u t r o n \approx 1.66 \times 10^{- 24} g$

3. What is the relationship between number of moles with volume?
Answer: 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.

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)

4. The number of atoms in a gramme?
Answer: Number of moles $\frac{w e i g h t o f s u b s t a n c e (g)}{M o l a r m a s s}$

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

Divide the sample's weight in grams by the periodic table's amu atomic mass, then multiply the result by $6.022 \times 10^{23}$ to find the sample's atomic composition.