Problem 77 - Chemistry: The Central Science

Question

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

Step-by-Step Solution

Answer

The osmotic pressure formed by dissolving \(44.2 mg\) of aspirin in \(0.358 L\) of water at \(25^{\circ} C\) is approximately \(0.345 atm\).

Step 1: Convert mass of aspirin to moles

First, we need to find the molar mass of aspirin, which is given by: \(Molar~ Mass = 9(12.01 g/mol) + 8(1.01 g/mol) + 4(16.00 g/mol)\).

Step 2: Calculate the moles of aspirin

Now, convert the given mass of aspirin (44.2 mg) to moles by dividing it by its molar mass in grams. Don't forget to convert milligrams to grams (\(1 grams = 1000 mg\)).

Step 3: Calculate the molarity of the aspirin solution

To find the concentration (molarity) of the aspirin solution, divide the moles of aspirin by the volume of the solution in liters (0.358 L): \(Molarity = \cfrac{moles~of~Aspirin}{volume~of~solution~in~L}\)

Step 4: Convert the temperature to Kelvin

The given temperature is in Celsius, but we need it in Kelvin for the osmotic pressure formula. To convert Celsius to Kelvin, add 273.15: \(Temperature (K) = Temperature (°C) + 273.15\)

Step 5: Calculate the osmotic pressure

Now that we have the molarity of the solution and the temperature in Kelvin, we can calculate the osmotic pressure using the formula: \(π = iMRT\) Plug in the values for \(i\) (1), molarity, temperature, and \(R\) (0.0821 L atm/mol K). Finally, multiply to find the osmotic pressure.

Key Concepts

Molarity

Molarity is a fundamental concept in chemistry, describing the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The formula for molarity is:\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]In the context of the exercise, after determining the moles of aspirin dissolved, you divide this value by the volume of the solution to find its molarity. Molarity allows chemists to understand and compare the concentrations of solutions, which is essential for experiments and reactions. Using molarity simplifies calculations involving solutions because it relates directly to the amount of chemical substance in a given volume.

Molar Mass

The molar mass of a compound is its mass per mole, usually expressed in grams per mole (g/mol). To calculate the molar mass of any compound, sum up the atomic masses of all atoms present in its molecular formula.For aspirin, with the molecular formula \(\text{C}_9\text{H}_8\text{O}_4\), the calculation involves the masses of carbon, hydrogen, and oxygen:

• Carbon: 9 atoms \(\times\) 12.01 g/mol
• Hydrogen: 8 atoms \(\times\) 1.01 g/mol
• Oxygen: 4 atoms \(\times\) 16.00 g/mol

Summing these values gives the molar mass of aspirin. This measurement is crucial because it allows for the conversion between the mass of the compound and the amount in moles, a necessary step for many chemical calculations, including determining solution concentrations.

Aspirin

Aspirin, chemically known as acetylsalicylic acid, is a widely used pharmaceutical. It is composed of carbon, hydrogen, and oxygen, with the molecular formula \(\text{C}_9\text{H}_8\text{O}_4\). Understanding its structure and formula is important to predict its reactivity and behavior in solutions.In the exercise, aspirin is used to determine the osmotic pressure when dissolved in water. Knowing the chemical composition and molecular weight helps calculate how much aspirin is present in moles, which is essential for finding the solution's molarity. Aspirin’s common use as a medication showcases its significance in both everyday life and scientific calculations.

Osmotic Pressure Formula

Osmotic pressure is an important property in chemistry, reflecting the pressure required to stop the flow of solvent into a solution through a semipermeable membrane. It's a key concept in areas ranging from lab work to biological systems.The equation for calculating osmotic pressure is:\[\pi = iMRT\]where:

• \(\pi\) = osmotic pressure in atm
• \(i\) = van 't Hoff factor (typically 1 for non-electrolytes like aspirin)
• \(M\) = molarity of the solution
• \(R\) = universal gas constant (0.0821 L atm/mol K)
• \(T\) = temperature in Kelvin

In the exercise, by using the given values and substituting them into the formula, you can calculate the osmotic pressure. This concept helps in understanding how solutions behave in different conditions and is useful in both practical applications and theoretical study.