Chapter 16: Problem 50
Pepsin is the principal digestive enzyme of gastric juice. A \(3.00\) -mg sample of pepsin is dissolved in enough water to make the \(10.0 \mathrm{~mL}\) of solution, and the osmotic pressure of the solution at \(25^{\circ} \mathrm{C}\) is found to be \(0.162\) Torr. Calculate the molecular mass of pepsin.
Short Answer
Step by step solution
Convert Osmotic Pressure to atm
Use the Osmotic Pressure Formula
Calculate Molarity (M)
Calculate Moles of Pepsin
Determine Molecular Mass
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molecular Mass Calculation
To find the molecular mass of a compound like pepsin, the mass of the sample was first measured - in this case, 3.00 mg or 0.00300 g. Then, using the calculated moles from the molarity and volume of the solution, the molecular mass equation is as follows:
- Use the equation: \( M = \frac{\text{mass}}{\text{moles}} \)
- Input the mass and the moles into the formula.
- Compute to find the molecular mass, which was approximately 34,500 g/mol in this case.
Van 't Hoff Factor
For non-ionizing compounds like the enzyme pepsin, the Van 't Hoff factor is \( i = 1 \). This indicates that the substance doesn't split into multiple particles in solution. This property simplifies our calculations as we don't need to factor in additional particles when dealing with enzymatic solutions.
Understanding the Van 't Hoff factor:
- For ionic compounds, \( i \) would be greater than 1, reflecting the number of ions produced.
- For non-ionic compounds, such as organic compounds like pepsin, \( i \) is 1.
- It's essential for accurately determining osmotic pressure, particularly in complex solutions.
Molarity
In the context of the pepsin solution, knowing the molarity is important for calculating various properties like osmotic pressure. The formula to find molarity is:
- \( M = \frac{\pi}{RT} \)
- Where \( \pi \) is osmotic pressure, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
- The calculated molarity from the pepsin exercise was approximately \( 8.70 \times 10^{-6} \text{ mol/L} \).