Question

What is the osmotic pressure formed by dissolving \(44.2 \mathrm{mg}\) of aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) in \(0.358\) L of water at \(25^{\circ} \mathrm{C}\) ?

Short answer

The osmotic pressure formed by dissolving 44.2 mg of aspirin in 0.358 L of water at 25°C is approximately 0.0169 atm.

Step-by-step solution

Convert the mass of aspirin into moles

To convert the mass of aspirin into moles, we need to find its molar mass first. The molar mass of aspirin (C9H8O4) can be calculated as the sum of the molar masses of its constituent elements: Molar mass of aspirin = (9 × 12.01) + (8 × 1.01) + (4 × 16.00) = 180.16 g/mol Now, we can find the number of moles of aspirin: Moles of aspirin = (mass of aspirin) / (molar mass of aspirin) Moles of aspirin = \( \frac{44.2 \space mg}{180.16 \space g/mol} (convert \space mg \space to \space g) = \frac{0.0442 \space g}{180.16 \space g/mol} \) Moles of aspirin ≈ 0.000245 mol

Find the molar concentration of aspirin in the solution

Now that we have the number of moles of aspirin, we can find the molar concentration (c) by dividing it by the volume of the solution in liters: c = \( \frac{moles \space of \space aspirin}{volume \space of \space solution} \) c = \( \frac{0.000245 \space mol}{0.358 \space L} \) c ≈ 0.000684 mol/L

Convert the temperature from Celsius to Kelvin

Temperature in Kelvin (T) = Temperature in Celsius + 273.15 T = 25°C + 273.15 T = 298.15 K

Calculate the osmotic pressure using the formula

Now we have everything we need to calculate the osmotic pressure using the formula: Osmotic Pressure (π) = i * c * R * T Since aspirin is a non-electrolyte, the van't Hoff factor (i) is 1. Using the values calculated above, we get: π = 1 * 0.000684 mol/L * 0.0821 L*atm/mol*K * 298.15 K π ≈ 0.0169 atm The osmotic pressure formed by dissolving 44.2 mg of aspirin in 0.358 L of water at 25°C is approximately 0.0169 atm.

Key concepts

Molar Mass Calculation

To determine the molar mass of a compound, you add the atomic masses of all atoms in its chemical formula. Atomic mass is typically given in atomic mass units (amu). For aspirin (\( \text{C}_9\text{H}_8\text{O}_4 \)), you have:

• 9 carbon atoms, each with an atomic mass of 12.01 amu
• 8 hydrogen atoms, each with an atomic mass of 1.01 amu
• 4 oxygen atoms, each with an atomic mass of 16.00 amu

To find the molar mass, use the formula:\[\text{Molar mass} = (9 \times 12.01) + (8 \times 1.01) + (4 \times 16.00)\]This gives a molar mass of 180.16 g/mol for aspirin. Molar mass converts the mass of a substance (in grams) to the amount (in moles) using the relationship:\[\text{Moles} = \frac{\text{mass in grams}}{\text{molar mass in g/mol}}\]For instance, converting 44.2 mg of aspirin to grams (0.0442 g) and using its molar mass:\[\text{Moles of aspirin} = \frac{0.0442}{180.16}\]This calculation tells you there are about 0.000245 moles of aspirin.

Moles and Molarity

Molarity is a way of expressing concentration by relating moles of solute to volume of solution in liters. It is denoted as \( c \) and calculated by:\[\text{Molarity } (c) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]This means if you know the moles of solute and the solution volume, you can find the molarity. For our aspirin example, with 0.000245 moles dissolved in 0.358 liters, the calculation becomes:\[c = \frac{0.000245\text{ mol}}{0.358\text{ L}}\]Resulting in a molarity of approximately 0.000684 mol/L. Molarity is crucial in reactions and calculations, such as finding osmotic pressure, because it gives a direct relationship between moles and volume of solution.

Temperature Conversion

Temperature conversion from Celsius to Kelvin is a simple yet essential step in scientific calculations, especially since many equations like the ideal gas law use Kelvin. To convert Celsius (\( ^\circ\text{C} \)) to Kelvin (\( \text{K} \)), use the equation:\[T(\text{K}) = T(^\circ\text{C}) + 273.15\]This conversion shifts the Celsius scale to start from absolute zero, which is the base point of the Kelvin scale. From our exercise, converting 25°C results in:\[T = 25 + 273.15 = 298.15\text{ K}\]Kelvin is preferred in scientific contexts because it avoids negative temperatures, simplifying many calculations. Always make sure to convert temperatures to Kelvin when using equations involving temperature to ensure accuracy.