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Chapter 13: Problem 77

What is the osmotic pressure formed by dissolving \(50.0 \mathrm{mg}\) of acetylsalicylic acid $\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\( in \)0.100 \mathrm{~L}\( of water at \)37^{\circ} \mathrm{C} ?$

Short Answer

Expert verified
The osmotic pressure formed by dissolving 50.0 mg of acetylsalicylic acid in 0.100 L of water at 37°C is approximately \(7.08 × 10⁻²\) atm.

Step by step solution

01

Calculate the molar mass of acetylsalicylic acid

To calculate the molar mass, we sum up the molar masses of all the atoms in acetylsalicylic acid (\(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\)). Molar mass of C: 12.01 g/mol Molar mass of H: 1.01 g/mol Molar mass of O: 16.00 g/mol Molar mass of acetylsalicylic acid = 9(12.01) + 8(1.01) + 4(16.00) = 180.16 g/mol
02

Determine the number of moles in the 50.0 mg sample

First, convert 50.0 mg to grams: 50.0 mg × 1 g/1000 mg = 0.0500 g Now, use the molar mass to find the number of moles: Number of moles = mass / molar mass = 0.0500 g / 180.16 g/mol = 2.77 × 10⁻⁴ mol
03

Calculate the molarity of the solution

Molarity (M) = number of moles / volume of solution in liters M = 2.77 × 10⁻⁴ mol / 0.100 L = 2.77 × 10⁻³ mol/L
04

Convert temperature from Celsius to Kelvin

To convert temperature from Celsius to Kelvin, we add 273.15 to the Celsius temperature: T(K) = 37°C + 273.15 = 310.15 K
05

Calculate the osmotic pressure

Use the osmotic pressure formula, remembering that van't Hoff factor (i) is 1 for non-electrolyte substances like acetylsalicylic acid: \( \Pi = iMRT \) Plug in the values: (M = 2.77 × 10⁻³ mol/L, R = 0.0821 L atm/mol K, and T = 310.15 K) \( \Pi = 1 × (2.77 × 10⁻³ \: \text{mol/L}) × (0.0821 \: \text{L atm/mol K}) × (310.15 \: \text{K}) \) \( \Pi = 7.08 × 10⁻² \: \text{atm} \) The osmotic pressure formed by dissolving 50.0 mg of acetylsalicylic acid in 0.100 L of water at 37°C is approximately 7.08 × 10⁻² atm.

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Most popular questions from this chapter

(a) What is the molality of a solution formed by dissolving 1.12 mol of KCl in 16.0 mol of water? (b) How many grams of sulfur \(\left(\mathrm{S}_{8}\right)\) must be dissolved in \(100.0 \mathrm{~g}\) of naphthalene $\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\( to make a \)0.12 \mathrm{~m}$ solution?

Indicate the type of solute-solvent interaction (Section 11.2) that should be most important in each of the following solutions: $(\mathbf{a}) \mathrm{CCl}_{4}\( in benzene \)\left(\mathrm{C}_{6} \mathrm{H}_{6}\right),(\mathbf{b})\( methanol \)\left(\mathrm{CH}_{3} \mathrm{OH}\right)\( in water, \)(\mathbf{c}) \mathrm{KBr}$ in water, (d) HCl in acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right).\)

A sulfuric acid solution containing \(697.6 \mathrm{~g}\) of $\mathrm{H}_{2} \mathrm{SO}_{4}\( per liter of solution has a density of \)1.395 \mathrm{~g} / \mathrm{cm}^{3} .$ Calculate (a) the mass percentage, \((\mathbf{b})\) the mole fraction, (c) the molality, \((\mathbf{d})\) the molarity of $\mathrm{H}_{2} \mathrm{SO}_{4}$ in this solution.

Suppose you had a balloon made of some highly flexible semipermeable membrane. The balloon is filled completely with a \(0.2 \mathrm{M}\) solution of some solute and is submerged in a 0.1 \(M\) solution of the same solute: Initially, the volume of solution in the balloon is \(0.25 \mathrm{~L}\). Assuming the volume outside the semipermeable membrane is large, as the illustration shows, what would you expect for the solution volume inside the balloon once the system has come to equilibrium through osmosis? [Section 13.5]

(a) A sample of hydrogen gas is generated in a closed container by reacting \(1.750 \mathrm{~g}\) of zinc metal with \(50.0 \mathrm{~mL}\) of $1.00 \mathrm{M}$ hydrochloric acid. Write the balanced equation for the reaction, and calculate the number of moles of hydrogen formed, assuming that the reaction is complete. (b) The volume over the solution in the container is 150 mL. Calculate the partial pressure of the hydrogen gas in this volume at $25^{\circ} \mathrm{C}$, ignoring any solubility of the gas in the solution. (c) The Henry's law constant for hydrogen in water at \(25^{\circ} \mathrm{C}\) is $7.7 \times 10^{-6} \mathrm{~mol} / \mathrm{m}^{3}-\mathrm{Pa}$. Estimate the number of moles of hydrogen gas that remain dissolved in the solution. What fraction of the gas molecules in the system is dissolved in the solution? Was it reasonable to ignore any dissolved hydrogen in part (b)?
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