Question

Calculate the weight of one atom of $ Ag $ . (Atomic weight of $ Ag = 108 $ )
(A) $ 17.93 \times {10^{ - 23}}{\text{gm}} $
(B) $ 16.93 \times {10^{ - 23}}{\text{gm}} $
(C) $ 17.93 \times {10^{23}}{\text{gm}} $
(D) $ 36 \times {10^{ - 23}}{\text{gm}} $

Answer 1

Hint: A convenient method of expressing the quantity of a substance is the mole concept. It is possible to break down any measurement into two parts: the numerical magnitude and the units in which the magnitude is expressed. We will solve this question by using the basic theory of mole concept.

Formula Used
In a given pure sample, the number of moles of a substance can be represented by the following formula:
 $ n = \dfrac{N}{{{N_A}}} $
Where
 $ n $ is the number of moles
 $ {N_A} $ is the Avogadro’s constant
 $ N $ is the total number of elementary entities.

Complete Step-by-Step solution
One mole of any entity is defined as the quantity of a substance containing exactly $ 6.023 \times {10^{23}} $ 'elementary entities' of the substance given.
So, one mole of any substance will be equal to $ 6.023 \times {10^{23}} $ entities.
Now, we know that one mole atoms of $ Ag $ weighs $ 108{\text{g}} $
That is,
Weight of $ 6.023 \times {10^{ - 23}} $ atoms of $ Ag = 108{\text{g}} $
Then, the weight of one atom of $ Ag $ will be given by
 $ \dfrac{{108}}{{6.023 \times {{10}^{ - 23}}}} $
Upon solving, we get
Weight of $ 1 $ atom of $ Ag = 17.93 \times {10^{ - 23}}{\text{g}} $
Hence, the correct option is (A).

Additional Information
The German chemist Wilhelm Ostwald introduced the word "mole" around the year $ 1896 $ deriving the term from the Latin word moles, meaning a 'heap' or 'pile. It is not always possible for the number of moles of a molecule to be equal to the number of moles of its constituent elements. A mole is the unit of measurement in the International System of Units for the quantity of substances.

Note
The number $ 6.023 \times {10^{23}} $ is commonly referred to as the constant of Avogadro and is often denoted by the ' $ {N_A} $ ' symbol. Atoms, molecules, monatomic/polyatomic ions, and other particles can be the fundamental entities that can be represented in moles (such as electrons).