/*! 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 58 Citric acid, \(\mathrm{H}_{3} \m... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 58

Citric acid, \(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\), occurs in plants. Lemons contain \(5 \%\) to \(8 \%\) citric acid by mass. The acid is added to beverages and candy. An aqueous solution is \(0.688 \mathrm{~m}\) citric acid. The density is \(1.049 \mathrm{~g} / \mathrm{mL}\). What is the molar concentration?

Short Answer

Expert verified
The molar concentration is approximately 0.663 M.

Step by step solution

01

Understand the Molarity and Molality

Molar concentration (molarity) \(M\) is given by the formula \(M = \frac{\text{moles of solute}}{\text{liters of solution}}\), while molality (\(m\)) is calculated as \(m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}\). The problem provides us the molality and requires us to find the molarity.
02

Calculate the Mass of the Solution

First, determine the mass of citric acid in 1 kg of solvent. Since the solution is \(0.688 \, ext{m}\), there are \(0.688\) moles of citric acid per \(1\) kg of solvent. Assume 1 kg of solvent to calculate the total mass of the solution.
03

Determine the Volume of the Solution

Using the density of the solution \(1.049 \, ext{g/mL}\), convert the mass of the solution to volume. If the solvent's mass is \(1000\) g (1 kg), and the solute's mass is \(0.688 imes 192.13 \, ext{g/mol} = 132.173 \, ext{g}\), the total mass of the solution is approximately \(1132.173 \, ext{g}\) (only considering solvent and solute). Calculate the volume using density formula: volume = \(\frac{\text{mass}}{\text{density}}\).
04

Calculate the Molarity

With the volume of the solution and the number of moles of solute known, use the molarity formula \(M = \frac{0.688}{\text{volume of solution in liters}}\) to calculate the molarity.

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.

Molar Concentration
Molar concentration, often referred to as molarity, is a fundamental concept in chemistry. It represents the number of moles of a solute present in one liter of solution. This unit is essential when measuring the strength or concentration of a solution. To calculate molar concentration (\(M\)), you use the formula:
  • \(M = \frac{\text{moles of solute}}{\text{liters of solution}}\)
This formula highlights two important aspects:
  • **Moles of solute**: Refers to the amount of substance present and can be calculated based on molar mass and given mass.
  • **Liters of solution**: Total volume of the solution where the solute is dissolved.
Using this formula requires the volume of the solution in liters, so it's often necessary to convert from milliliters if that's the initial volume you have. Understanding molarity is crucial for predicting how substances will react in solution.
Molality
Molality, represented with the symbol (\(m\)), measures the concentration of a solution based on the mass of the solvent rather than the total volume. This unit makes it useful for studies involving temperature variations, as it does not depend on the solution's volume (which can expand or contract with temperature).Molality is calculated using the formula:
  • \(m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}\)
The key components here are:
  • **Moles of solute**: Just like with molarity, molality considers how many moles of the solute are present.
  • **Kilograms of solvent**: This is the mass of the solvent alone, not the total mass of the solution.
Because it is based on mass, molality remains constant regardless of environmental factors, such as temperature, making it reliable for certain calculations.
Density of Solution
Density is an important property of solutions that influences how concentration calculations are approached. It is defined as the mass of the solution per unit volume, often expressed in grams per milliliter (g/mL). The formula for density is:
  • \( \text{Density} = \frac{\text{mass of solution}}{\text{volume of solution}} \)
Applications of density include:
  • **Conversion between mass and volume**: Knowing the density lets you convert from the mass of a solution to its volume, which can be necessary for finding molar concentration.
  • **Determining solution properties**: Helps to understand how concentrated a solution is based on given conditions, which is key in various industrial and scientific applications.
In this context, having the density allows for converting the total mass of the solution into the volume, which is crucial for calculating molarity.

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

Dextran is a polymeric carbohydrate produced by certain bacteria. It is used as a blood plasma substitute. An aqueous solution contains \(0.582 \mathrm{~g}\) of dextran in \(106 \mathrm{~mL}\) of solution at \(21^{\circ} \mathrm{C}\). It has an osmotic pressure of \(1.47 \mathrm{mmHg}\). What is the average molecular weight of the dextran?

The lattice enthalpy of sodium chloride, \(\Delta H^{\circ}\) for $$ \mathrm{NaCl}(s) \longrightarrow \mathrm{Na}^{+}(g)+\mathrm{Cl}^{-}(g) $$ is \(787 \mathrm{~kJ} / \mathrm{mol}\); the heat of solution in making up \(1 \mathrm{M} \mathrm{NaCl}(a q)\) is \(+4.0 \mathrm{~kJ} / \mathrm{mol}\). From these data, obtain the sum of the heats of hydration of \(\mathrm{Na}^{+}\) and \(\mathrm{Cl}^{-}\). That is, obtain the sum of \(\Delta H^{\circ}\) values for $$ \begin{aligned} &\mathrm{Na}^{+}(g) \longrightarrow \mathrm{Na}^{+}(a q) \\ &\mathrm{Cl}^{-}(g) \longrightarrow \mathrm{Cl}^{-}(a q) \end{aligned} $$ If the heat of hydration of \(\mathrm{Cl}^{-}\) is \(-338 \mathrm{~kJ} / \mathrm{mol}\), what is the heat of hydration of \(\mathrm{Na}^{+}\) ?

A \(55-\mathrm{g}\) sample of a gaseous fuel mixture contains \(0.51\) mole fraction propane, \(\mathrm{C}_{3} \mathrm{H}_{8}\); the remainder of the mixture is butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\). What are the masses of propane and butane in the sample?

Aluminum hydroxide forms a positively charged sol. Which of the following ionic substances should be most effective in coagulating the sol? a. \(\mathrm{NaCl}\) b. \(\mathrm{CaCl}_{2}\) c. \(\mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) d. \(\mathrm{K}_{3} \mathrm{PO}_{4}\)

What mass of solution containing \(5.00 \%\) potassium iodide, KI, by mass contains \(258 \mathrm{mg}\) KI?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

Kinetics

Read Explanation

Inorganic 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.