Question

20 grams of sodium hydroxide is dissolved in 180g of water. Find the mole fraction of each components

Answer 1

Answer:

Mole fraction of NaOH = 0.05

Mole fraction of H₂O = 0.95

Explanation:

$\diamond$ We know that,

$\implies$ Number of moles = $\dfrac{Given \ mass}{Molar \ mass}$

$\implies$ Mole Fraction = $\dfrac{Number \ of \ moles}{Total \ number \ of \ moles}$

$\diamond$ Given that,

$\implies$ Given Mass of NaOH = 20g

$\implies$ Molar mass of NaOH = 23 + 16 + 1

                                          = 40 g

$\implies$ Given mass of H₂O = 180g

$\implies$ Molar mass of H₂O = 2 + 16

                                       = 18g

$\diamond$ Therefore,

$\implies$ Number of moles of NaOH = $\dfrac{20}{40} = \dfrac{1}{2} = 0.5$

$\implies$ Number of moles of H₂O = $\dfrac{180}{18} = \dfrac{10}{1} = 10$

$\diamond$ Hence,

$\implies$ Total number of moles = 0.5 + 10

                                             = 10.5

$\diamond$ Mole fraction of NaOH = $\dfrac{Number \ of \ moles \ of \ NaOH}{Total \ number \ of \ moles}$

                                      = $\dfrac{0.5}{10.5} =\dfrac{5}{105} =\dfrac{1}{21} \approx 0.047$ $\approx 0.05$

$\diamond$ Mole fraction of H₂O = $\dfrac{Number \ of \ moles\ of \ H_2O}{Total \ number \ of \ moles }$

                                   = $\dfrac{10}{10.5} =\dfrac{100}{105} = \dfrac{20}{21} \approx 0.95$