Question

A man writes his biodata with a carbon pencil on the paper having mass 150 mg. After writing his biodata, he weighs the written paper and finds its mass 152 mg. What is the number of carbon atoms present in the paper?
A.$1.0036 \times {10^{20}}$
B.$5.02 \times {10^{20}}$
C.$1.0036 \times {10^{23}}$
D.$0.502 \times {10^{20}}$

Answer 1

Here, first we have to calculate the mass of carbon in paper and then we have to use Avogadro's number to calculate the number of carbon atoms. We know that a mole of anything consists of $6.022 \times {10^{23}}$ particles (Avogadro’s number).

Complete step by step answer:

First, we have to calculate the mass of carbon in paper. Given that, before writing, the weight of paper is 150 mg and after writing the weight of the paper is 152 mg. So, the mass of carbon can be calculated by subtracting the mass of paper before writing from the mass of paper after writing.

Mass of paper$= 152\,{\rm{mg}} - {\rm{150}}\,{\rm{mg}} = {\rm{2}}\,{\rm{mg}}$

In gram, the mass of carbon is $= \dfrac{2}{{1000}} = 0.002\;{\rm{g}}$

We know that, mass of carbon is 12 g.

Now, we have to calculate the moles of carbon in the paper. We know the formula to calculate moles is,

${\rm{Number}}\,{\rm{of}}\,{\rm{moles}} = \dfrac{{{\rm{Mass}}}}{{{\rm{Molar}}\,{\rm{mass}}}}$
…… (1)

Now, we have to put mass=0.002 g and molar mass 12 g in equation (1).

${\rm{Number}}\,{\rm{of}}\,{\rm{moles}}\,{\rm{of carbon}} = \dfrac{{0.002\,{\rm{g}}}}{{12\,{\rm{g}}\,{\rm{mo}}{{\rm{l}}^{ - 1}}}} = \dfrac{1}{{6000}}{\rm{mol}}$

We know that 1 mole of anything contains $6.022 \times {10^{23}}$ number of atoms. Now, using the unitary method, number of atoms in $\dfrac{1}{{6000}}{\rm{mol}}$ of carbon is,

$\Rightarrow {\rm{Number}}\,{\rm{of carbon atoms}} = 6.022 \times {10^{23}} \times \dfrac{1}{{6000}}$

$\Rightarrow {\rm{Number}}\,{\rm{of}}\,{\rm{carbon}}\,{\rm{atoms}} = 1.0036 \times {10^{20}}$

Additional Information:

The number $6.022 \times {10^{23}}$ is named in honor of the Italian physicist Amedeo Avogadro. The Avogadro's number aids in counting very small particles. Different kinds of particles, such as molecules, atoms, ions, electrons are representative particles. One mole of anything consists of $6.022 \times {10^{23}}$ representative particles. For example, one mole of oxygen consists of $6.022 \times {10^{23}}$ molecules of oxygen. Hence, the relation between mole and Avogadro’s number is $1\;{\rm{mol}} = 6.022 \times {10^{23}}\;{\rm{particles}}$

Note:
Always remember that, the mole or mol (abbreviation form) is the unit which measures the amount of substance present. A mole is the term that defines the number of carbon (C) atoms in 12 g of pure carbon.