Question

If one $mole$ of carbon atoms weighs $12grams$ then what is the mass of one atom of carbon (in $grams$) :
A. $1.993 \times {10^{23}}grams$
B. $1.993 \times {10^{ - 23}}grams$
C. $1.993 \times {10^{24}}grams$
D. $1.993 \times {10^{ - 24}}grams$

Answer 1

The question can be solved using mole concept. It states that one mole of any element or compound contains a specific number of entities that is Avogadro’s Number of entities. We shall calculate the moles of carbon and thus the total particles present. Then we shall calculate the mass of one particle.

Complete step by step answer:
Avogadro Constant is the proportionality factor which defines the relationship between the number of constituent particles such as molecules, atoms or ions in a sample with the amount of substance in that sample.
${N_A} = 6.022 \times {10^{23}}mo{l^{ - 1}}$
Where,
${N_A}$= Avogadro Constant
As, one $mole$ of a sample has $6.022 \times {10^{23}}$ number of constituent particles (molecules, atoms or ions).
So, $1mole$ of carbon has $6.022 \times {10^{23}}$atoms.
According to the question,
One $mole$ of carbon weighs $12grams$
We can write as,
$\Rightarrow 6.022 \times {10^{23}}$ atoms of carbon weighs $12grams$
So, one atom of carbon weighs = $\dfrac{{12}}{{6.022 \times {{10}^{23}}}}grams$
$\Rightarrow 1.993 \times {10^{ - 23}}grams$
Hence, Option B is correct.

Additional Information:
The Avogadro number (or constant) has been defined in many different ways through its long history. Its approximate value was first determined, indirectly, by Josef Loschmidt in $1865$(Avogadro's number is closely related to the Loschmidt constant and the two concepts are sometimes confused.)
It was initially defined by Jean Perrin as the number of atoms in $16grams$of oxygen. It was later redefined in the 14th conference of the International Bureau of Weights and Measures (BIPM) as the number of atoms in $12grams$ of the isotope $carbon - 12$ $({C^{12}})$.
In each case, the $mole$ was defined as the quantity of a substance that contained the same number of atoms as those reference samples. In particular, when $carbon - 12$ was the reference, one $mole$ of $carbon - 12$ was exactly $12grams$ of the element.

Note:
The numeric value of the Avogadro constant expressed in reciprocal $mol$ $(mo{l^{ - 1}})$ , a dimensionless number, is called the Avogadro number, sometimes denoted by $N$ or ${N_0}$ which is thus the number of particles that are contained in one $mole$, exactly $6.02214076 \times {10^{23}}$.