Question

0.302 grams of an antibiotic was dissolved in 500 mL of water at 23.6°C. The solution has an osmotic pressure of 8.34 mm Hg. What is the molar mass of the antibiotic?

Answer 1

To find the molar mass of the unknown compound, use the osmotic pressure and temperature to calculate the molarity. Then, use the molarity to find the moles of solute and finally, use the moles of solute and the molar mass formula to find the mass of the unknown compound.

Step-by-step explanation:

To find the molar mass of the unknown compound, we can use the formula:

Molarity (M) = moles of solute / liters of solution

In this case, we have the osmotic pressure and temperature, which allows us to use the formula:

Π = MRT

Where Π is the osmotic pressure, M is the molarity, R is the ideal gas constant, and T is the temperature in Kelvin.

Rearranging the formula to solve for molarity, we get:

M = Π / (RT)

Plugging in the given values, we have:

M = (0.025 atm) / (0.0821 L·atm/mol·K * 275 K)

M = 0.00117 M

Next, we can use the molarity to find the moles of the unknown compound:

moles of solute = Molarity × volume of solution

moles of solute = 0.00117 M * 0.00105 L = 1.23 × 10^-6 mol

Finally, we can use the moles of solute and the molar mass formula to find the mass of the unknown compound:

Mass = moles of solute × molar mass

Mass = 1.23 × 10^-6 mol × 46.06 g/mol = 5.67 × 10^-5 g