A solution contains 3.95g of CS2 and 2.43g CH3COCH3.vapor pressures at 35°C of pure CS2 and pure CH3COCH3 are 616 torr and 332 torr respectively.Assume ideal ,calculate vapor pressure of each component n the total vapor pressure?
1 Answer
The total vapor pressure is
Explanation:
This problem requires you to have some idea about Raoult's Law, which allows you to calculate the partial vapor pressure of a liquid that's part of a mixture by using the vapor pressure of the pure substance and its mole fraction in the mixture.
#color(blue)(P_"A" = chi_"A" * P_"A"^@)" "# , where
You need to use the molar masses of the two substances to find how many moles of each you have. For carbon disulfide you have
#3.95color(red)(cancel(color(black)("g"))) * "1 mole"/(76.13color(red)(cancel(color(black)("g")))) = "0.0519 moles CS"""_2#
For acetone, you have
#2.43color(red)(cancel(color(black)("g"))) * "1 mole"/(58.08color(red)(cancel(color(black)("g")))) = "0.0418 moles"# #("CH"""_3)_2"CO"#
The total number of moles in the mixture is
#n_"total" = n_(CS_2) + n_((CH_3)_2CO)#
#n_"total" = 0.0519 + 0.0418 = "0.0937 moles"#
The mole fraction of carbon sulfide is
#chi_(CS_2) = n_(CS_2)/n_"total"#
#chi_(CS_2) = (0.0519color(red)(cancel(color(black)("moles"))))/(0.0937color(red)(cancel(color(black)("moles")))) = "0.554"#
The mole fraction of acetone is
#chi_"acetone" = n_"acetone"/n_"total"#
#chi_"acetone" = (0.0418color(red)(cancel(color(black)("moles"))))/(0.0937color(red)(cancel(color(black)("moles")))) = "0.446"#
This means that the partial vapor pressure of carbon disulfide is
#P_(CS_2) = chi_(CS_2) * P_(CS_2)^@#
#P_(CS_2) = 0.554 * "616 torr" = color(green)("341 torr")#
The partial vapor pressure of acetone will be
#P_"acetone" = 0.446 * "332 torr" = color(green)("148 torr")#
The total vapor pressure will be
#P_"total" = P_(CS_2) + P_"acetone"#
#P_"total" = "341 torr" + "148 torr" = color(green)("489 torr")#
