# Question #9e925

##### 1 Answer

Here's what I got.

#### Explanation:

The **osmotic pressure** of an aqueous solution can be calculated by using the equation

#color(blue)(ul(color(black)(Pi = i * c * RT)))#

Here

#Pi# is the osmotic pressure of the solution#i# is the van't Hoff factor#c# is themolarityof the solution#R# is the universal gas constant, usually given as#0.0821("atm" * "L")/("mol" * "K")# #T# is theabsolute temperatureof the solution

Now, you didn't provide a value for the temperature of the solution, so I'll just assume that you're working at room temperature

#T = 20^@"C" + 273.15 = "293.15 K"#

You know that the van't Hoff factor is said to be equal to

#Pi = c * RT#

Rearrange to solve for

#c = Pi/(RT)#

Plug in your values to find

#c = (0.037 color(red)(cancel(color(black)("atm"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * "L")/("mol" * color(red)(cancel(color(black)("K")))) * 293.15color(red)(cancel(color(black)("K")))) = "0.001537 mol L"^(-1)#

Use the molarity and the volume of the solution, which you can assume to be equal to the volume of water, to determine the *number of moles* of solute present in the solution

#0.200 color(red)(cancel(color(black)("L solution"))) * "0.001537 moles solute"/(1color(red)(cancel(color(black)("L solution")))) = "0.0003074 moles solute"#

To find the **molar mass** of the protein, use the fact that **moles**

#1 color(red)(cancel(color(black)("mole protein"))) * "5.00 g"/(0.0003074color(red)(cancel(color(black)("moles protein")))) = "16,265 g"#

Since the molar mass of the protein tells you the mass of **mole** of this protein, you can say that you will have

#color(darkgreen)(ul(color(black)(M_"M protein" = "16,300 g mol"^(-1))))#

I'll leave the answer rounded to three **sig figs**, but keep in mind that you only have two sig figs for the osmotic pressure.