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Multiple Choice
0.302 grams of an antibiotic was dissolved in enough water at 23.6°C to make 500.0 mL of solution. The solution has an osmotic pressure of 8.34 mm Hg. What is the molar mass of the antibiotic?
A
350 g/mol
B
250 g/mol
C
150 g/mol
D
450 g/mol
Verified step by step guidance
1
First, understand that osmotic pressure (π) can be calculated using the formula: π = (n/V)RT, where n is the number of moles, V is the volume in liters, R is the ideal gas constant, and T is the temperature in Kelvin.
Convert the given osmotic pressure from mm Hg to atm, since the ideal gas constant R is typically used in atm. Use the conversion: 1 atm = 760 mm Hg.
Convert the temperature from Celsius to Kelvin using the formula: T(K) = T(°C) + 273.15.
Rearrange the osmotic pressure formula to solve for the number of moles (n): n = (πV)/(RT). Substitute the values for π (in atm), V (in liters), R (0.0821 L·atm/mol·K), and T (in Kelvin) into the equation.
Finally, calculate the molar mass of the antibiotic by dividing the mass of the antibiotic (0.302 grams) by the number of moles calculated in the previous step. Molar mass = mass/n.