Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 13: Problem 126

NaCl(aq) isotonic with blood is \(0.92 \%\) NaCl (mass/volume). For this solution, what is (a) \(\left[\mathrm{Na}^{+}\right]\) (b) the total molarity of ions; (c) the osmotic pressure at \(37^{\circ} \mathrm{C} ;\) (d) the approximate freezing point? (Assume that the solution has a density of 1.005 g/mL.)

Short Answer

Expert verified
The molarity of Na+ is 0.157 M, the total molarity of ions in the solution is 0.314 M, the osmotic pressure at 37 °C is 19.1 atm, and the approximated freezing point will be lower than 0°C and can be calculated based on the formula for freezing point depression and the given parameters in the problem statement.

Step by step solution

01

Calculate Molarity of Na+

Molarity is calculated as moles of solute per liter of solution. First calculate the moles of NaCl. The solution is 0.92% NaCl by mass/volume. So, 100 mL of this solution contains 0.92g of NaCl. Moles = Mass/Molar mass: Moles of NaCl = 0.92 g / 58.44 g/mol = 0.0157 mol. Then divide this by the volume of the solution in liters: Molarity of NaCl = 0.0157 mol / 0.1 L = 0.157 M.
02

Calculate Total Molarity of Ions

Each NaCl unit dissociates into one Na+ ion and one Cl- ion in solution. Since the molarity of NaCl is 0.157 M, the total molarity of ions will be 2 * 0.157 M = 0.314 M.
03

Calculate Osmotic Pressure

Since we know the total molarity of ions and if we take R = 0.0821 L.atm/(K.mol), the osmotic pressure can be calculated using the formula: 'osmotic pressure = i * n * R * T'. Here i = 2 (ionisation factor for NaCl), n is the molarity of ions we calculated in the previous step, and T is the absolute temperature in Kelvin: Osmotic Pressure = 2 * 0.314 mol/L * 0.0821 L.atm/K.mol * (37 °C + 273 K) = 19.1 atm.
04

Calculate Freezing Point

NaCl is a strong electrolyte and will fully dissociate into its ions in a solution. In this case, the van’t Hoff factor (i) is 2. Using the equation for freezing point depression, which is ΔT = i * Kf * m, where ΔT is the depression in freezing point, Kf is the cryoscopic constant (which is 1.86 °C/kg for water), and m is the molality of the solution. We'll use the calculated moles of NaCl and the mass of the solution (weight of 100mL water is approx 100g, or 0.1kg) to find molality, then substitute all values into the equation to calculate ΔT. It's worth noting that the freezing point of a solution will always be lower than that of the pure solvent.

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

At \(25^{\circ} \mathrm{C}\) a \(0.50 \mathrm{g}\) sample of polyisobutylene (a polymer used in synthetic rubber) in \(100.0 \mathrm{mL}\) of benzene solution has an osmotic pressure that supports a \(5.1 \mathrm{mm}\) column of solution \((d=0.88 \mathrm{g} / \mathrm{mL}) .\) What is the molar mass of the polyisobutylene? (For \(\mathrm{Hg}\), \(d=13.6 \mathrm{g} / \mathrm{mL} .)\)

Calculate the mole fraction of solute in the following aqueous solutions: (a) \(21.7 \% \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH},\) by mass; (b) \(0.684 m \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\) (urea).

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 \(1027 \mathrm{kg} / \mathrm{m}^{3}\).

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?

Adding \(1.00 \mathrm{g}\) of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) to \(80.00 \mathrm{g}\) cyclohexane, \(\mathrm{C}_{6} \mathrm{H}_{12},\) lowers the freezing point of the cyclohexane from 6.5 to \(3.3^{\circ} \mathrm{C}\). (a) What is the value of \(K_{f}\) for cyclohexane? (b) Which is the better solvent for molar mass determinations by freezing- point depression, benzene or cyclohexane? Explain.
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Organic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

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