If 4 g of NaOH dissolves in 36 g of `H_(2)O`, calculate the mole fraction of each component in the solution. Also, determine the molarity of solution (specific gravity of solution is `1 g mL^(-1)`).

Explanation

Number of moles of NaOH,
`n_(NaOH)= (4)/(40) = 0.1` mol `{n=("Mass(g)")/("Molar mass")}`
Similarly, `n_(H_(2)O)=(36)/(18)=2` mol
Mole fraction of solute
`X_(NaOH) = ("moles of NaOH")/("moles of NaOH" + "moles of "H_(2)O)`
`X_(NaOH)=(0.1)/(0.1+2)=0.0476`
`X_(H_(2)O)=(n_(H_(2)O))/(n_(NaOH)+n_(H_(2)O))`
`=(2)/(0.1+2)=0.9524`
Total mass of solution `=("mass of solute")+("mass of solvent")`
`=4+36=40g`
Volume of solution `=("Mass of solution")/("Specific gravity")`
`=(40g)/(1g mL^(-1))=40 mL`
Molarity `=("Moles of solute " xx 1000)/("Volume of solution(mL)")`
`=(0.1xx1000)/(40) = 2.5M`