How many number of molecules are there in 10 grams of nitric acid (HNO3)?

Wednesday, March 16, 2011

How many number of molecules are there in 10 grams of nitric acid (HNO3)?

Hello!

By definition, there are about $\displaystyle{6}\cdot{{10}}^{{{23}}}$ molecules in each mole of any substance. This number is called Avogadro number and is usually denoted as $\displaystyle{N}_{{A}}.$ If we'll find the number of moles in $\displaystyle{10}$ grams of nitric acid, we'll know the number of molecules by multiplying it by $\displaystyle{N}_{{A}}.$

Atoms of each type have its own mass. This mass, expressed in grams per mole, may be found in many sources including the periodic table. The values for $\displaystyle{H},$ $\displaystyle{N}$ and $\displaystyle{O}$ should be memorized and are about $\displaystyle{1},$ $\displaystyle{14}$ and $\displaystyle{16}$ grams per mole, respectively. Therefore the mass of one molecule of $\displaystyle{H}{N}{O}_{{3}}$ is $\displaystyle{1}+{14}+{3}\cdot{16}={63}{\left(\frac{{g}}{{{m}{o}{l}}}\right)}.$

Hence we have $\displaystyle\frac{{{10}{g}}}{{{63}{\left(\frac{{g}}{{{m}{o}{l}}}\right)}}}\approx{0.16}{m}{o}{l}$ of nitric acid, and the number of molecules is about $\displaystyle{6}\cdot{{10}}^{{{23}}}\cdot{0.16}\approx{0.95}\cdot{{10}}^{{{23}}}={9.5}\cdot{{10}}^{{{22}}}.$ This is the answer.