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Chapter 13: Problem 73

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

Expert verified
The osmotic pressure formed by dissolving 44.2 mg of aspirin in 0.358 L of water at 25掳C is approximately \(1.689 \: atm\).

Step by step solution

01

Write down the osmotic pressure formula

The osmotic pressure formula is derived from the ideal gas law and is given by: \(螤 = \dfrac{n}{V} RT\) where: - 螤 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鈦宦� mol鈦宦�) - T is the temperature in Kelvin
02

Convert temperature to Kelvin

The given temperature is in Celsius. Therefore, we need to convert it to Kelvin. The conversion formula is: \(K = 掳C + 273.15\) So, \(T = 25掳C + 273.15 = 298.15 K\)
03

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) = \(9 脳 M_{C} + 8 脳 M_{H} + 4 脳 M_{O}\) 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: \(n = \dfrac{44.2 \times 10^{-3} \: g}{180.16 \: g/mol} = 2.452 \times 10^{-4} \: mol\)
04

Calculate the osmotic pressure

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

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Most popular questions from this chapter

(a) What is the mass percentage of iodine \(\left(\mathrm{I}_{2}\right)\) in a solution containing \(0.035 \mathrm{~mol} \mathrm{I}_{2}\) in \(115 \mathrm{~g}\) of \(\mathrm{CCl}_{4} ?\) (b) Seawater contains \(0.0079 \mathrm{~g} \mathrm{Sr}^{2+}\) per kilogram of water. What is the concentration of \(\mathrm{Sr}^{2+}\) measured in \(\mathrm{ppm} ?\)

Which of the following in each pair is likely to be more soluble in water: (a) cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right)\) or glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) (Figure 13.12); (b) propionic acid \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\right)\) or sodium propionate \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COONa}\right) ;\) (c) \(\mathrm{HCl}\) or ethyl chloride \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}\right) ?\) Explain in each case.

Water and glycerol, \(\mathrm{CH}_{2}(\mathrm{OH}) \mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2} \mathrm{OH}\), are mis- cible in all proportions. What does this mean? How do the OH groups of the alcohol molecule contribute to this miscibility?

Calculate the number of moles of solute present in each of the following aqueous solutions: (a) \(600 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{SrBr}_{2}\), (b) \(86.4 \mathrm{~g}\) of \(0.180 \mathrm{~m} \mathrm{KCl}\), (c) \(124.0 \mathrm{~g}\) of a solution that is \(6.45 \%\) glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) by mass.

The solubility of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20{ }^{\circ} \mathrm{C}\) is \(70 \mathrm{~g}\) per \(100 \mathrm{~mL}\) of water. (a) \(\mathrm{ls}\) a \(1.22 \mathrm{M}\) solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) in water at \(20^{\circ} \mathrm{C}\) saturated, supersaturated, or unsaturated? (b) Given a solution of \(\mathrm{MnSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}\) of unknown concentration, \(w\) hat experiment could you perform to determine whether the new solution is saturated, supersaturated, or unsaturated?
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