Question #6ffde

1 Answer
Jun 3, 2016

Answer:

#M_M = 4.39 * 10^4"g mol"^(-1)#

Explanation:

Osmotic pressure is simply the pressure that must be applied to a solution in order to prevent the incoming flow of water through a semipermeable membrane.

chemwiki.ucdavis.edu

You can derive the equation that gives you the osmotic pressure of a solution that contains a non-electrolyte solute by using the ideal gas law equation

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#, where

#P# - the pressure of the gas
#V# - the volume it occupies
#n# - the number of moles of gas
#R# - the universal gas constant, usually given as #0.0821("atm" * "L")/("mol" * "K")#
#T# - the absolute temperature of the gas

Isolate #P# on one side of the equation to get

#P = n/V * RT#

Now, you know that the number of moles of solute per volume of solution gives you the molarity of the solution

#color(purple)(|bar(ul(color(white)(a/a)color(black)(c = n_"solute"/V_"solution")color(white)(a/a)|)))#

Plug this into the above equation to get the osmotic pressure, #Pi#

#color(blue)(|bar(ul(color(white)(a/a)Pi = c * RTcolor(white)(a/a)|)))#

Now, let's say that #M_Mcolor(white)(a)"g mol"^(-1)# is the molar mass of this protein. You can express the number of moles of solute in solution by writing

#n = (30.0 color(red)(cancel(color(black)("g"))))/(M_Mcolor(red)(cancel(color(black)("g")))"mol"^(-1)) = 30.0/M_Mcolor(white)(a)"moles"#

You thus have

#Pi = 30.0/M_M * 1/V * RT#

Isolate #M_M# on one side of the equation, convert the temperature from degrees Celsius to Kelvin, and plug in your values to get

#M_M = 30.0/Pi * (RT)/V#

#M_M = (30.0 color(red)(cancel(color(black)("moles"))))/(0.0167color(red)(cancel(color(black)("atm")))) * (0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * (273.15 + 25)color(red)(cancel(color(black)("K"))))/(1.00 color(red)(cancel(color(black)("L"))))#

#M_M = "43,919"#

I'll leave the answer rounded to three sig figs and expressed in scientific notation

#M_M = color(green)(|bar(ul(color(white)(a/a)color(black)(4.39 * 10^4 "g mol"^(-1))color(white)(a/a)|)))#