/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 A \(1.5\) M \(\mathrm{NaCl}\) so... [FREE SOLUTION] | 91影视

91影视

A \(1.5\) M \(\mathrm{NaCl}\) solution and a \(0.75 \mathrm{M} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\) solution exist on opposite sides of a semipermeable membrane. Determine the osmolarity of each solution and the direction of solvent flow, if any, across the membrane.

Short Answer

Expert verified
No solvent flow; both solutions have an osmolarity of 3.0 Osm/L.

Step by step solution

01

Calculate Osmolarity of NaCl Solution

To find the osmolarity of the NaCl solution, we need to consider that NaCl dissociates into Na鈦 and Cl鈦 ions when dissolved in water. Thus, for each mole of NaCl, there are 2 osmoles in solution (1 for Na鈦 and 1 for Cl鈦). Given that the concentration is 1.5 M, the osmolarity is \(1.5 \, M \times 2 = 3.0\, \text{Osm}\/\text{L}\).
02

Calculate Osmolarity of Al(NO鈧)鈧 Solution

Al(NO鈧)鈧 dissociates into one Al鲁鈦 ion and three NO鈧冣伝 ions, making a total of 4 osmoles per mole of Al(NO鈧)鈧. Therefore, the osmolarity of a 0.75 M solution is \(0.75\, M \times 4 = 3.0\, \text{Osm}\/\text{L}\).
03

Determine the Direction of Solvent Flow

Water will move from a region of lower osmolarity to a region of higher osmolarity. In this problem, both solutions have the same osmolarity of 3.0 Osm/L. Therefore, since there's no osmolarity difference, there will be no net movement of solvent across the membrane.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Semipermeable Membrane
A semipermeable membrane is a very selective barrier. It allows certain substances to pass through, while blocking others. In the context of our exercise, it allows the passage of the solvent (like water) but not the solutes (like sodium chloride or aluminum nitrate).
Understanding how it works is important in explaining osmotic pressure and solvent flow.
These membranes are often used in processes like dialysis or water filtration where it is crucial to separate different types of molecules from each other.
  • Membranes can be made from natural materials, like cellular membranes, or synthetic, used in lab environments.
  • The idea is to mimic biological processes where only essential substances pass, while others stay back due to size or charge restrictions.
In our problem, solutions of NaCl and Al(NO鈧)鈧 are separated by such a membrane. It's why the movement of molecules needs to be considered carefully to predict solvent flow.
Solvent Flow
Solvent flow, especially in osmosis, is a fundamental concept in chemistry and biology. It refers to the movement of a solvent from an area of low solute concentration to an area of high solute concentration through a semipermeable membrane.
This movement occurs to balance concentrations on both sides. Think of it as nature's way of achieving equilibrium.
  • This process doesn't require external energy, making it a type of passive transport.
  • Solvent flow stops when osmotic pressure (the pressure that needs to be applied to stop the flow) is equal on both sides or when concentrations are equal.
In the original exercise, both solutions have the same osmolarity. Therefore, there's no net solvent flow, showcasing a state of equilibrium.
Dissociation of Compounds
The dissociation of compounds involves splitting molecules into ions when dissolved in a solvent.
This is critical for calculating osmolarity, which helps us understand the concentration of solute particles in a solution.
Different compounds dissociate into different numbers of ions:
  • NaCl dissociates into two ions: \( ext{Na}^+ \) and \( ext{Cl}^- \). Thus, its dissociation contributes 2 osmoles per mole.
  • Al(NO鈧)鈧 dissociates into four ions: one \( ext{Al}^{3+} \) and three \( ext{NO}_3^{-} \). Therefore, each mole gives 4 osmoles.
This process is crucial because osmolarity directly influences osmotic pressure. Understanding dissociation allows us to predict the properties of solutions accurately, as seen in the step-by-step solution where the calculation of osmolarity is essential in determining any possible solvent flow across the membrane.

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

How much water must be added to \(25.0 \mathrm{~mL}\) of a \(1.00 \mathrm{M} \mathrm{NaCl}\) solution to make a resulting solution that has a concentration of \(0.250 \mathrm{M} ?\)

In each pair of aqueous systems, which will have the higher boiling point? a. \(0.50 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) or \(1.0 \mathrm{M} \mathrm{KBr}\) b. \(1.5 \mathrm{M} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) or \(0.75 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}\) c. \(0.10 \mathrm{M} \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) or pure water

Calcium nitrate reacts with sodium carbonate to precipitate solid calcium carbonate: $$ \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2(a q)}+\mathrm{Na}_{2} \mathrm{CO}_{3(a q)} \rightarrow \mathrm{CaCO}_{3(s)}+\mathrm{NaNO}_{3(a q)} $$ a. Balance the chemical equation. b. How many grams of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) are needed to react with \(50.0 \mathrm{~mL}\) of \(0.450 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) ? c. Assuming that the \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) has a negligible effect on the volume of the solution, find the osmolarity of the \(\mathrm{NaNO}_{3}\) solution remaining after the \(\mathrm{CaCO}_{3}\) precipitates from solution.

Two solutions are separated by a semipermeable membrane. Solution A contains \(25.0 \mathrm{~g}\) of \(\mathrm{NaCl}\) in \(100.0 \mathrm{~mL}\) of water and solution B contains \(35.0 \mathrm{~g}\) of \(\mathrm{NaCl}\) in \(100.0 \mathrm{~mL}\) of water. a. Which one has a higher concentration? b. Which way will water molecules flow? c. Which volume will increase? d. Which volume will decrease? e. What will happen to the concentration of solution \(\mathrm{A}\) ? f. What will happen to the concentration of solution \(\mathrm{B}\) ?

Will solutions of each solute conduct electricity when dissolved? a. \(\mathrm{AgNO}_{3}\) b. \(\mathrm{CHCl}_{3}\) c. \(\mathrm{BaCl}_{2}\) d. \(\mathrm{Li}_{2} \mathrm{O}\)

See all solutions

Recommended explanations on Chemistry Textbooks

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.