The osmotic pressure of a solution containing 5.00 mg of an unknown protein per 10

mL of solution was 2.73 torr at 25 °C. Find the molar mass of the unknown protein.

To find the molar mass of the unknown protein, we need to use the formula relating osmotic pressure and molar mass:

\[ \Pi = \frac{n}{V}RT \]

Where:
- Π is the osmotic pressure,
- n is the number of moles of solute,
- V is the volume of the solution,
- R is the ideal gas constant, and
- T is the temperature in Kelvin.

Since osmotic pressure is given in torr and temperature is given in degrees Celsius, we need to convert them to the appropriate units.

First, let's convert the temperature from Celsius to Kelvin:

\[ T = 25 + 273.15 = 298.15 \, \text{K} \]

Next, let's calculate the number of moles of the solute using the given mass and the molar mass (M) of the protein:

\[ n = \frac{\text{mass}}{M} \]

We can rearrange this equation to solve for the molar mass (M) of the protein:

\[ M = \frac{\text{mass}}{n} \]

Substituting the given values:

\[ M = \frac{5.00 \times 10^{-3} \, \text{g}}{n} \]

Since we need the value of n to solve for M, we can rewrite the gas equation to solve for n:

\[ n = \frac{\Pi V}{RT} \]

Now, substitute the given values into the equation:

\[ n = \frac{2.73 \, \text{torr} \times 10 \, \text{mL}}{0.0821 \, \text{L} \cdot \text{atm/mol} \cdot \text{K} \times 298.15 \, \text{K}} \]

Make sure all units are consistent. We converted mL to L and torr to atm to maintain consistency.

Now, we have the value of n, and we can substitute it into our equation for the molar mass:

\[ M = \frac{5.00 \times 10^{-3} \, \text{g}}{2.73 \, \text{torr} \times 10 \, \text{mL} \times 0.0821 \, \text{L} \cdot \text{atm/mol} \cdot \text{K} \times 298.15 \, \text{K}} \]

Simplifying, we get:

\[ M = \frac{5.00 \times 10^{-3}}{2.73 \times 10 \times 0.0821 \times 298.15} \, \text{g/mol} \]

Calculating this will give us the molar mass of the unknown protein.

pi = MRT

Substitute and solve for molarity, M.
Then M = moles/L
You know M and L, solve for moles, then
moles = g/molar mass. Solve for molar mass.