Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Problem 54

Calculate the vapor pressure at \(20^{\circ} \mathrm{C}\) of a saturated solution of the nonvolatile solute, urea, \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2},\) in methanol, \(\mathrm{CH}_{3} \mathrm{OH} .\) The solubility is \(17 \mathrm{g}\) urea/100 \(\mathrm{mL}\) methanol. The density of methanol is \(0.792 \mathrm{g} / \mathrm{mL}\), and its vapor pressure at \(20^{\circ} \mathrm{C}\) is \(95.7 \mathrm{mmHg}\).

Short Answer

Expert verified
After performing these calculations, you would find the vapor pressure of the saturated solution at \(20^{\circ} \mathrm{C}\).

Step by step solution

01

Calculation of moles

We first need to calculate the moles of methanol and urea in the solution. The molar mass of methanol is \(32.04 \, \mathrm{g/mol}\) and that of urea is \(60.06 \, \mathrm{g/mol}\). Knowing that there are 17g of urea in 100 mL of the solution and the density of methanol is \(0.792 \, \mathrm{g/mL}\), we get Moles of urea = \(\frac{17 \, \mathrm{g}}{60.06 \, \mathrm{g/mol}}\) Moles of methanol = \(\frac{100 \, \mathrm{mL} \times 0.792 \, \mathrm{g/mL}}{32.04 \, \mathrm{g/mol}}\)
02

Calculation of mol fraction

The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all solution components. So, the mole fraction of methanol, \(X_{CH3OH}\), will be \(X_{CH3OH} = \frac{\text{Moles of methanol}}{\text{Moles of methanol} + \text{Moles of urea}}\)
03

Application of Raoult's Law

Raoult's Law states that the vapor pressure of a solvent above a solution is equal to the mole fraction of the solvent times the vapor pressure of the pure solvent. This can be expressed as \(P_{solution} = X_{solvent} \times P_{solvent}\)Substituting the calculated mole fraction of methanol and the given vapor pressure of pure methanol (\(95.7 \, \mathrm{mmHg}\)):\(P_{solution} = X_{CH3OH} \times 95.7 \, \mathrm{mmHg}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the concentration of an isotonic saline solution, \(0.92 \% \mathrm{NaCl}(\mathrm{mass} / \text { volume }),\) to determine the osmotic pressure of blood at body temperature, \(37.0^{\circ} \mathrm{C}\). [Hint: Assume that \(\mathrm{NaCl}\) is completely dissociated in aqueous solutions.]

A 0.72 g sample of polyvinyl chloride (PVC) is dissolved in \(250.0 \mathrm{mL}\) of a suitable solvent at \(25^{\circ} \mathrm{C}\). The solution has an osmotic pressure of \(1.67 \mathrm{mm} \mathrm{Hg}\). What is the molar mass of the PVC?

Explain the important distinctions between each pair of terms: (a) molality and molarity; (b) ideal and nonideal solution; (c) unsaturated and supersaturated solution; (d) fractional crystallization and fractional distillation; (e) osmosis and reverse osmosis.

The Environmental Protection Agency has a limit of 15 ppm for the amount of lead in drinking water. If a \(1.000 \mathrm{mL}\) sample of water at \(20^{\circ} \mathrm{C}\) contains \(15 \mathrm{ppm}\) of lead, how many lead ions are there in this sample of water? What is the mole fraction of lead ion in solution?

What is the molarity of \(\mathrm{CO}_{2}\) in a liter of ocean water at \(25^{\circ} \mathrm{C}\) that contains approximately \(280 \mathrm{ppm}\) of \(\mathrm{CO}_{2} ?\) The density of ocean water is \(1027 \mathrm{kg} / \mathrm{m}^{3}\).
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Reactions

Read Explanation

Organic Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free