A solution of two components containing n₁ moles of the 1^st component and n₂ moles of the 2^nd component is prepared. M₁ and M₂ are the molecular weights of component 1 and 2 respectively. If d is the density of the solution in g mL^–1, C₂ is the molarity and x₂ is the mole fraction of the 2^nd component, then C₂ can be expressed as :

<table class="tg"> <thead> <tr> <th class="tg-baqh"></th> <th class="tg-baqh"><b>1^st component</b></th> <th class="tg-baqh"><b>2^nd component</b></th> </tr> </thead> <tbody> <tr> <td class="tg-baqh"><b>Mole</b></td> <td class="tg-baqh">n₁</td> <td class="tg-baqh">n₂</td> </tr> <tr> <td class="tg-baqh"><b>Molecular<br>Weight</b></td> <td class="tg-baqh">M₁</td> <td class="tg-baqh">M₂</td> </tr> <tr> <td class="tg-baqh"><b>Mass</b></td> <td class="tg-baqh">n₁M₁</td> <td class="tg-baqh">n₂M₂</td> </tr> </tbody> </table> <br><br>Mass of solution = n₁M₁ + n₂M₂ <br><br>density of the solution = d <br><br>C₂ = Molarity of 2^nd Component <br><br>x₂ = Mole-fraction of 2^nd Component <br><br>x₂ = ${{{n_2}} \over {{n_1} + {n_2}}}$ <br><br>$\Rightarrow$ 1 - x₂ = ${{{n_1}} \over {{n_1} + {n_2}}}$ <br><br>Molarity of 2^nd Component, <br><br>C₂ = <span style="display: inline-block;vertical-align: middle;"> <div style="text-align: center;border-bottom: 1px solid black;">n₂</div> <div style="text-align: center;">Volume of solution(ml)</div> </span> $\times$ 1000 <br><br>= $${{{n_2}} \over {{{Mass\,of\,Solution(ml)} \over {Density\,of\,Solution(g/ml)}}}} \times 1000$$ <br><br>= ${{d \times {n_2} \times 1000} \over {{n_1}{M_1} + {n_2}{M_2}}}$ <br><br>= $${{d \times {{{n_2}} \over {{n_1} + {n_2}}} \times 1000} \over {{{{n_1}} \over {{n_1} + {n_2}}}{M_1} + {{{n_2}} \over {{n_1} + {n_2}}}{M_2}}}$$ (Dividing componendo and dividendo by n₁ + n₂) <br><br>= $${{d \times {x_2} \times 1000} \over {\left[ {\left( {1 - {x_2}} \right){M_1} + {x_2}{M_2}} \right]}}$$ <br><br>= ${{1000d{x_2}} \over {{M_1} + {x_2}\left( {{M_2} - {M_1}} \right)}}$