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 \(1.689 \: atm\).

Step-by-step solution

Write down the osmotic pressure formula

The osmotic pressure formula is derived from the ideal gas law and is given by: \(Π = \dfrac{n}{V} RT\) where: - Π is the osmotic pressure - n is the number of moles of solute (aspirin) - V is the volume of the solution in liters - R is the ideal gas constant (0.0821 L atm K⁻¹ mol⁻¹) - T is the temperature in Kelvin

Convert temperature to Kelvin

The given temperature is in Celsius. Therefore, we need to convert it to Kelvin. The conversion formula is: \(K = °C + 273.15\) So, \(T = 25°C + 273.15 = 298.15 K\)

Find moles of solute (aspirin)

To find the moles of aspirin, we will use the formula: \(n = \dfrac{m}{M}\) where: - m is the mass of aspirin in grams - M is the molar mass of aspirin First, convert the mass of aspirin to grams: \(44.2 \: mg = 44.2 \times 10^{-3} \: g\) Next, calculate the molar mass of aspirin: M (aspirin) = \(9 × M_{C} + 8 × M_{H} + 4 × M_{O}\) where \(M_{C}\), \(M_{H}\), and \(M_{O}\) are the molar masses of carbon, hydrogen, and oxygen, respectively. M (aspirin) = \(9(12.01 \: g/mol) + 8(1.01 \: g/mol) + 4(16.00 \: g/mol) = 180.16 \: g/mol\) Now we can find the moles of aspirin: \(n = \dfrac{44.2 \times 10^{-3} \: g}{180.16 \: g/mol} = 2.452 \times 10^{-4} \: mol\)

Calculate the osmotic pressure

Now we have all the values required to calculate the osmotic pressure formed by dissolving aspirin in water: Π = \(\dfrac{2.452 \times 10^{-4} \: mol}{0.358 \: L} \times 0.0821 \: \dfrac{L \: atm}{K \: mol} \times 298.15 \: K\) Π = \(1.689 \: atm\) So, the osmotic pressure formed by dissolving 44.2 mg of aspirin in 0.358 L of water at 25°C is approximately 1.689 atm.