The mass percent of pentane has been 22.55%. The mole fraction of pentane has been 0.387. The molality of pentane has been 7.34 m. The molarity of pentane in the solution has been 3.11 M.
The mass percent has been the amount of pentane present in total volume of solution. The mass of pentane has been derived from density as:
[tex]\rm Density=\dfrac{mass}{volume}[/tex]
[tex]\rm 0.63=\dfrac{mass}{25} \\mass=0.63\;\times\;25\;g\\mass=15.75\;g[/tex]
The mass of pentane in solution has been 15.75g.
The mass percent of pentane in the solution has been given as the mass divided by total volume of solution.
[tex]\rm Mass\%=\dfrac{15.75}{25\;+\;45}\;\times\;100 \\Mass\%=\dfrac{15.75}{70}\;\times\;100 \\Mass\%=22.5\%[/tex]
The mass percent of pentane has been 22.55%.
[tex]\rm Moles=\dfrac{mass}{molar\;mass}[/tex]
The mass of pentane has been 15.75 g. The moles of pentane have been given by:
[tex]\rm Moles\;pentane=\dfrac{15.75}{72.15} \\Moles\;pentane=0.218\;mol[/tex]
The moles of pentane in solution has been 0.218 mol.
The moles of hexane in solution has been given by first calculating the mass of hexane from density:
[tex]\rm 0.66=\dfrac{mass}{45} \\mass=0.66\;\times\;45\\mass=29.7\;g[/tex]
The mass of hexane has been 29.7 g. The moles of hexane have been calculated as:
[tex]\rm Moles\;hexane=\dfrac{29.7}{86.18}\\Moles\;hexane=0.344\mol[/tex]
The moles of hexane in solution has been 0.344 mol.
The total moles of the solution has been:
[tex]\rm Moles\;=0.218\;+\;0.344\\Moles=0.562[/tex]
The total moles of solution has been 0.562 moles.
The mole fraction of pentane has been:
[tex]\rm Mole\;fraction=\dfrac{0.218}{0.562}\\Mole\;fraction=0.387[/tex]
The mole fraction of pentane has been 0.387.
[tex]\rm Mass\;solution=29.7\;+\;15.75\;g\\Mass\;solution=45.45\;g\\Mass\;solution=0.045\;kg[/tex]
The molality (m) of pentane in the solution has been:
[tex]m=\rm \dfrac{moles\;solute}{mass\;solvent}[/tex]
Substituting the value for molality of pentane:
[tex]\textit m=\rm \dfrac{0.218}{0.0297\;kg\;hexane}\\\textit m= 7.34\;m[/tex]
The molality of pentane has been 7.34 m.
[tex]M=\rm \dfrac{moles\;solute}{Volume\;solution\;(L)}[/tex]
Substituting the value for molarity of pentane:
[tex]M=\dfrac{0.218}{0.07}\\M=3.11\;\rm M[/tex]
The molarity of pentane in the solution has been 3.11 M.
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