A solution containing 27.55 mg of an unknown protein per 25.0 mL solution was found to have an

step 1 Okay. This problem is quizzing us on the osmotic pressure of a solution containing a protein wit

A solution containing 27.55 mg of an unknown protein per...

A solution containing $27.55 \mathrm{mg}$ of an unknown protein per $25.0 \mathrm{~mL}$ solution was found to have an osmotic pressure of 3.22 torr at $25^{\circ} \mathrm{C} .$ What is the molar mass of the protein?

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Key Concepts

Molarity and Molar Mass Determination

Molarity, defined as the number of moles of solute per liter of solution, is directly calculated from experimental conditions. By determining the moles of solute present through mass measurements and comparing this with the concentration inferred from osmotic pressure measurements, one can deduce the molar mass of the solute. This process is crucial for characterizing unknown substances, such as proteins, in solution.

Unit Conversion

Accurate calculations using the van’t Hoff equation require careful conversion of units to maintain consistency. This typically involves converting the temperature from Celsius to Kelvin and altering the osmotic pressure from units like torr to atmospheres to match the units used in the gas constant, R, ensuring the mathematical validity of the relationship.

Van't Hoff Equation

The van’t Hoff equation, ? = MRT, relates the osmotic pressure (?) of a solution to its molarity (M), absolute temperature (T), and the universal gas constant (R). This equation serves as a fundamental tool in determining properties such as the molar mass of solutes in dilute solutions by linking the measurable osmotic pressure to the concentration of solute particles.

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