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6. Chemical Quantities & Aqueous Reactions
Osmolarity
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0.0201 g of aspirin is dissolved in enough water to produce a 100.0 mL solution. The osmotic pressure of this solution is 0.0271 atm at 301 K. Aspirin has a van't Hoff factor of 1. Determine the molar mass of aspirin.
A
200 g/mol
B
180 g/mol
C
250 g/mol
D
150 g/mol
Verified step by step guidance1
Start by using the formula for osmotic pressure: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor, \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
Given that the van't Hoff factor \( i \) is 1, the osmotic pressure \( \Pi \) is 0.0271 atm, the temperature \( T \) is 301 K, and \( R \) is 0.0821 L·atm/mol·K, substitute these values into the equation to solve for molarity \( M \): \( 0.0271 = 1 \times M \times 0.0821 \times 301 \).
Rearrange the equation to solve for \( M \) (molarity): \( M = \frac{0.0271}{0.0821 \times 301} \).
Once you have the molarity, use the definition of molarity \( M = \frac{n}{V} \), where \( n \) is the number of moles and \( V \) is the volume in liters. Here, \( V = 0.100 \) L. Rearrange to find \( n \): \( n = M \times 0.100 \).
Finally, calculate the molar mass of aspirin by using the formula: \( \text{Molar mass} = \frac{\text{mass of solute}}{n} \), where the mass of solute is 0.0201 g. Substitute the values to find the molar mass.
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