Question #ea892
1 Answer
You need to add
Explanation:
The idea here is that you need to figure out what mole fraction of water is needed in order for the solution to have a vapor pressure 0.595 mmHg smaller than that of pure water.
You know that the vapor pressure for a volatile component of a solution is
#color(blue)(P_i = chi_i * P_i^@)" "# , where
So, the vapor pressure of the solution must be
#P = P_"water"^@ - "0.595 mmHg"#
#P = "17.5 mmHg" - "0.595 mmHg" = "16.905 mmHg"#
Since water is the only volatile component, you can say that
#P = chi_"water" * P_"water"^@ implies chi_"water" = P/P_"water"^@#
This means that the mole fraction of water in the solution must be
#chi_"water" = (16.905color(red)(cancel(color(black)("mmHg"))))/(17.5color(red)(cancel(color(black)("mmHg")))) = "0.966"#
The mole fraction of water is simply the ratio between the number of moles of water and the total number of moles present in the solution.
#chi_"water" = n_"water"/n_"total"#
The total number of moles in the solution will be
#n_"total" = n_"water" + n_"sucrose"#
This means that you have
#chi_"water" = n_"water"/(n_"water" + n_"sucrose") implies n_"sucrose" = n_"water"/chi_"water" - n_"water"#
Use water's molar mass to find the number of moles of water
#661color(red)(cancel(color(black)("g"))) * "1 mole"/(18.015color(red)(cancel(color(black)("g")))) = "36.692 moles"#
This means that the solution must contain
#n_"sucrose" = 36.692/0.966 - 36.692 = "1.291 moles sucrose"#
Now use sucrose's molar mass to see how many grams would contain this many moles
#1.291color(red)(cancel(color(black)("moles"))) * "342.29 g"/(1color(red)(cancel(color(black)("mole")))) = color(green)("442 g")#