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 \(0.358 \mathrm{~L}\) 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 0.0168 atm.

Step-by-step solution

Calculate the moles of aspirin

To calculate the moles of aspirin, we will first find the molar mass of aspirin (C9H8O4) which can be derived by finding the sum of the atomic masses of each of its elements. Molar Mass of Aspirin = 9(Mass of C) + 8(Mass of H) + 4(Mass of O) = 9(12) + 8(1) + 4(16) = 180 g/mol Now we can convert the mass of aspirin (44.2 mg) to grams and then calculate the moles of aspirin: \(44.2mg * \frac{1g}{1000mg} = 0.0442g\) Moles of Aspirin = Mass of Aspirin / Molar Mass of Aspirin Moles of Aspirin = 0.0442 g / 180 g/mol = 0.000245 mol

Calculate the molarity of the aspirin solution

Now that we have the moles of aspirin, we can calculate the molarity by dividing the moles by the volume of water in liters. Molarity = Moles of Aspirin / Volume of Water Molarity = 0.000245 mol / 0.358 L = 0.000684 M

Convert the temperature to Kelvin

To use the osmotic pressure formula, we need the temperature in Kelvin. Convert the given temperature from Celsius to Kelvin: Temperature in Kelvin = Temperature in Celsius + 273.15 Temperature in Kelvin = 25 + 273.15 = 298.15 K

Calculate the osmotic pressure

Now we have all the necessary values to calculate the osmotic pressure using the formula: Osmotic Pressure = Molarity × R × T Osmotic Pressure = 0.000684 M × 0.0821 L atm/mol K × 298.15 K = 0.0168 atm The osmotic pressure formed by dissolving 44.2 mg of aspirin in 0.358 L of water at 25°C is approximately 0.0168 atm.

Key concepts

Molarity Calculation

Molarity, often represented by the unit M, is a measure of concentration in chemistry describing the number of moles of a solute per liter of solution. It plays a key role in quantifying the concentration of compounds in a solution, which is essential for various calculations, including determining osmotic pressure.

To calculate molarity, the formula used is:
\[\begin{equation} \text{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \end{equation}\]
For students to grasp this concept effectively, it's practical to break down the process: First, determine the number of moles of the substance using its weight and molar mass. Then, divide this value by the volume of the solution where the substance is dissolved.

This calculation is fundamental in chemistry as it helps in creating solutions of consistent concentration, essential to many experiments and reactions. When teaching molarity, it is effective to illustrate with examples how the concentration impacts the properties of a solution and how it relates to osmotic pressure in biological and chemical systems.

Molar Mass of Compounds

The molar mass of a compound is a crucial concept in chemistry that refers to the mass of one mole of a given substance. Usually expressed in grams per mole (g/mol), it is the sum of the atomic masses of all the atoms in a molecule.

To find the molar mass, you should look up each element's atomic mass on the periodic table and then use the following formula:
\[\begin{equation}\text{Molar Mass of Compound} = \sum (\text{Number of atoms of each element} \times \text{Atomic mass of element})\end{equation}\]
For example, for aspirin \[\begin{equation} \text{(C}_{9}\text{H}_{8}\text{O}_{4})\end{equation}\],you would sum up the atomic masses for carbon (C), hydrogen (H), and oxygen (O) multiplied by their respective number of atoms in the molecule.

Understanding the molar mass is essential for calculating the moles of a compound when given its mass, which is a step towards performing more advanced calculations like molarity and determining osmotic pressure. Clear examples with different compounds can help students cement their understanding of how to calculate molar mass effectively.

Colligative Properties

Colligative properties are physical properties of solutions that depend on the number of dissolved particles, such as ions or molecules, rather than their identity. These properties include vapor pressure lowering, freezing point depression, boiling point elevation, and osmotic pressure.

Osmotic pressure, in particular, is the pressure required to stop the flow of a solvent through a semipermeable membrane separating two solutions of different concentrations. It is a critical concept for fields like biology and medicine, as it explains the movement of water and solutes across cell membranes.
The formula for osmotic pressure \[\begin{equation}(\Pi)\end{equation}\] is given by:
\[\begin{equation}\Pi = MRT\end{equation}\]
where \[\begin{equation}M\end{equation}\] is the molarity of the solution, \[\begin{equation}R\end{equation}\] is the ideal gas constant, and \[\begin{equation}T\end{equation}\] is the temperature in Kelvin. Demonstrating colligative properties in the classroom can be enhanced by conducting experiments to show how different solutes affect the physical properties of the solvent. This tangible approach gives students a better understanding of the abstract concept of colligative properties and its implications in real-world phenomena.