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 \(0.0168 \, \text{atm}\).

Step-by-step solution

1. Convert mass of aspirin to moles

First, we need to find the molecular weight of aspirin. Aspirin has a chemical formula of C_9 H_8 O_4, so the molecular weight can be found as follows: Molecular weight (MW) = (9 * atomic weight of C) + (8 * atomic weight of H) + (4 * atomic weight of O) MW = (9 * 12.01 g/mol) + (8 * 1.01 g/mol) + (4 * 16.00 g/mol) MW = 108.09 g/mol + 8.08 g/mol + 64.00 g/mol MW = 180.17 g/mol Now, we can convert the given mass of aspirin to moles: moles = mass / MW moles = 44.2 mg * (1 g / 1000 mg) / 180.17 g/mol moles = 0.000245 mol

2. Convert temperature to Kelvin

The given temperature is 25°C, which can be converted to Kelvin using the formula T(K) = T(°C) + 273.15: T = 25°C + 273.15 T = 298.15 K

3. Calculate the osmotic pressure

Using the osmotic pressure formula mentioned earlier, we can now calculate the osmotic pressure: π = (n/V) * R * T We're given the volume of the solution (V = 0.358 L), we determined the number of moles (n = 0.000245 mol) and the temperature in Kelvin (T= 298.15 K), and the ideal gas constant (R = 0.0821 L atm / mol K). Plugging these values into the formula: π = (0.000245 mol / 0.358 L) * 0.0821 L atm / mol K * 298.15 K π = 0.0168 atm

4. Final 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.

Key concepts

Molar Mass of Aspirin

Understanding how to calculate the molar mass of a compound is essential in chemistry, and in this case, it's the first step in determining the osmotic pressure of an aspirin solution. Aspirin, medically known as acetylsalicylic acid, has a specific chemical formula: \( C_9H_8O_4 \) which indicates it is composed of carbon (C), hydrogen (H), and oxygen (O) atoms.
To determine the molar mass of aspirin, we sum the masses of all the atoms in one molecule. The atomic weights of carbon, hydrogen, and oxygen are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively. Multiplying these by the number of each type of atom in a molecule of aspirin and adding them up gives us the molar mass:
\[ \text{Molar mass of aspirin} = (9 \times 12.01 \text{ g/mol}) + (8 \times 1.01 \text{ g/mol}) + (4 \times 16.00 \text{ g/mol}) = 180.17 \text{ g/mol} \]
Having the molar mass allows us to convert a known mass of aspirin into moles, which then plays a key role in the calculation of osmotic pressure.

Mole Calculation

The mole is a fundamental unit in chemistry that represents a specific amount of particles—typically atoms, molecules, or ions. Understanding mole calculations is critical since it helps relate the physical mass of a substance to its number of particles, which is crucial in many chemical equations and processes.
Using the molar mass of aspirin calculated previously, we can convert the mass of aspirin to moles. The relationship between mass, molar mass, and moles is expressed by the equation:
\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]
For our aspirin example, where the mass in milligrams must first be converted to grams (since molar mass is in grams per mole), the calculation of moles of aspirin would be:
\[ \text{moles of aspirin} = \frac{44.2 \text{ mg} \times (1 \text{ g} / 1000 \text{ mg})}{180.17 \text{ g/mol}} = 0.000245 \text{ mol} \]
This value is then used to determine the concentration of aspirin in the solution, leading us towards calculating osmotic pressure.

Temperature Conversion to Kelvin

In scientific measurements, especially when dealing with gas laws and solutions, temperature must often be expressed in Kelvin (K). Kelvin is the SI base unit of temperature that is used in the ideal gas law and related calculations. Unlike Celsius or Fahrenheit, Kelvin starts at absolute zero, meaning 0 K is the theoretical point where particles have no thermal motion.
To convert Celsius to Kelvin, which is needed for our osmotic pressure calculation, add 273.15 to the Celsius temperature:
\[ T(K) = T(^\circ C) + 273.15 \]
For an aspirin solution at \(25^\circ C\), the conversion to Kelvin is straight-forward:
\[ T = 25^\circ C + 273.15 = 298.15 K \]
This gives us the necessary temperature value in the appropriate unit for use in the osmotic pressure equation.

Ideal Gas Constant Application

The ideal gas constant (R) is a proportionality factor in the ideal gas law and other equations that relate the amount of gas, pressure, temperature, and volume. In osmotic pressure calculations, we assume the solution behaves similarly to an ideal gas, allowing us to use the gas constant.
The value of R is 0.0821 L atm / mol K when pressure is in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and the amount in moles (mol). Plugging in our calculated moles, converted temperature, and given volume into the osmotic pressure equation:
\[ \pi = \left(\frac{n}{V}\right) \times R \times T \]
we determine the osmotic pressure created by the aspirin solution:
\[ \pi = \left(\frac{0.000245 \text{ mol}}{0.358 \text{ L}}\right) \times 0.0821 \text{ L atm / mol K} \times 298.15 \text{ K} = 0.0168 \text{ atm} \]
This application of the ideal gas constant bridges the gap between molar amounts and observable physical properties like osmotic pressure.