CHEM 1C Lecture Notes - Lecture 5: Rate Equation, Equilibrium Constant, Chemical Equilibrium

The reversible chemical reaction

A+B⇌C+D

has the following equilibrium constant:

Kc=[C][D]/[A][B]=7.5

Part A

Initially, only A and B are present, each at 2.00 M. What is the final concentration of A once equilibrium is reached?

Express your answer to two significant figures and include the appropriate units.

Part B

What is the final concentration of D at equilibrium if the initial concentrations are [A] = 1.00 M and [B] = 2.00 M ?

Express your answer to two significant figures and include the appropriate units.

2)

Learning Goal:

To determine equilibrium concentrations from initial conditions.

The reversible reaction

XY(aq)⇌X(aq)+Y(aq)

has a reaction quotient Qc defined as

Qc=[X][Y]/[XY]

Because the reaction is reversible, both the forward and reverse reactions will occur simultaneously. The reaction will eventually reach equilibrium, at which point the concentrations do not change, and Qc is equal to a constant known as Kc.

Calculating equilibrium concentrations when the net reaction proceeds forward

Consider mixture B, which will cause the net reaction to proceed forward.

Concentration (M)initial:change:equilibrium:[XY]0.500−x0.500−xnet→⇌[X]0.100+x0.100+x+[Y]0.100+x0.100+x

The change in concentration, x, is negative for the reactants because they are consumed and positive for the products because they are produced.

Part B

Based on a Kc value of 0.180 and the given data table, what are the equilibrium concentrations of XY, X, and Y, respectively?

Express the molar concentrations numerically.

Calculating equilibrium concentrations when the net reaction proceeds in reverse

Consider mixture C, which will cause the net reaction to proceed in reverse.

Concentration (M)initial:change:equilibrium:[XY]0.200+x0.200+x←net⇌[X]0.300−x0.300−x+[Y]0.300−x0.300−x

The change in concentration, x, is positive for the reactants because they are produced and negative for the products because they are consumed.

Part C

Based on a Kc value of 0.180 and the data table given, what are the equilibrium concentrations of XY, X, and Y, respectively?

Express the molar concentrations numerically.

Please, provide complete explanation.

© Division of Chemical Educatio

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• Vol.

86 No.

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In the Classroom

Self-heating or self-cooling containers for meals and bever

-

ages are excellent examples of chemistry in action for the every

-

day life of consumers. Such containers consist of dual chambers

where the food is usually contained in the internal chamber

while the chemical process that would heat or cool the food or

beverage occurs in the other. A common cooling system consists

of ammonium nitrate and water while a common heating system

consists of the reaction of calcium oxide in water. The heating

or cooling chamber requires the reagents to be separated until

ready to use.

These hydration methods are simple and do impart heat

effects; however, they present some limitations such as heat

-

ing times of 5–15 minutes (required to generate the necessary

temperature increases) and the need for large amounts of the

reagents because of the low heat energ y yield, which then must

occupy a considerable space in the containers. Emerging tech

-

nologies are making self-heating foods more accessible to the

general public. One such technolog y is the self-propagating

high-temperature synthesis (SHS) that involves the oxidation of

a mixture of aluminum and other metals by iron oxide, Fe

2

O

3

.

The change in enthalpy of this reaction is greater than 3 kJ/g

of reactants, making it more than 4 times higher than the heat

energ y evolved when limestone reacts with water

(1).

This tech

-

nolog y ensures heating a beverage from 2–3 °C to the boiling

point in less than 90 seconds and cutting the heating time for

food to less than four minutes.

In Spain and other European countries self-heating bever

-

ages are known as “autocalentables” and are easily found at gas

stations, airports, and highway rest stops. A variety of these

products are available including different types of coffee (black,

with milk, or cappuccino), chocolate, and tea. In the United

States commercialization of these food products has been tar

-

geted toward outdoors enthusiasts and the military; however,

companies such as Starbucks and Wolfgang Puck are advancing

into this market. In the 1980s the U.S. Army took the lead to

further develop the technolog y required to enhance the Meals,

Ready to Eat or MREs that were used a decade earlier by the U.S.

Space Program. One of these advancements included the Flame

-

less Ration Heater (FRH) that allows military troops in combat

to have a hot meal. These MREs, which include snacks, main

entrees, and desserts, are now sold through a number of online

sites and are available individually or in packages of “emergency

supply” or “disaster preparedness” units

(2).

These products provide an excellent means to promote

interest in chemistry. The activity described in this article uses

these commercial products to study the chemistry that produces

the self-heating mechanism. Concepts such as stoichiometry,

enthalpy of reaction, enthalpy of solution, heat transfer, and

density of liquids are the core principles involved in these reac

-

tions. Creative ways to use these products may also be discussed.

For example, the FRH of the MREs have been used in combat

situations to warm intravenous fluids before administering them

to patients as deployed medical units often do not have means to

heat these fluids and by doing so they may prevent hypothermia

in patients

(3).

Methodology

We have used this activity with two different method

-

ologies in the classroom: as the foundation for problem-based

learning (PBL) and as the framework for inquir y-g uided

instruction (IGI). Even though this activity could be easily

performed in the laboratory, it has been designed, tested, and

implemented as a classroom activity where calculations and

evaluation of results take precedence to data collection. In the

PBL methodolog y the acquisition of skills and knowledge arise

from the need to solve a problem related to the background

or experience of the students. The expected learning depends

primarily on the collective reflection of a group of students.

The role of the instructor is to meet with the group of students

primarily as a listener and when necessary pose questions to

lead students in the right direction. In PBL the problem is

loosely constructed but the goal is clearly stated. PBL has

received prominent emphasis in health-related careers

(4–6),

but its benefits have been documented in a variety of disciplines

(7–10)

and academic levels of instruction

(11–14).

IGI adopts

a more structured approach where student learning is promoted

through the use of questions meant to initiate the curiosity of

the students to get them started on finding answers to their own

questions

(15, 16).

Both methodologies rely on group work

where students collectively think, reflect, and provide ways

by which to solve a problem. The instructor facilitates these

processes rather than informing students what needs to be done

next. This activity is presented using both methodologies so that

instructors may choose the one that better fits their pedagogical

goals or teaching styles.

The Chemistry of Self-Heating Food Products

An Activity for Classroom Engagement

Maria T. Oliver-Hoyo*

Department of Chemistry, North Carolina State University, Raleigh, NC 27695; *

[email protected]

Gabriel Pinto

E.T.S. de Ingenieros Industriales, Universidad Politécnica de Madrid, 28006 Madrid, Spain

Juan Antonio Llorens-Molina

E.T.S. del Medio Rural y Enología, Universidad Politécnica de Valencia, 46010 Valencia, Spain

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In the Classroom

The design of this activity fulfills the common elements

these methodologies share along with what Duch identifies as

practical criteria for a “good” problem

(17)

:

• “hooking”

the student

to spark

interest

and

motivation

preferably within a real-life context

• requiring

reflection

as students

recognize

and explain

how

to proceed, discerning which information is relevant and

necessary at each stage of the solving process

• relying

on group

thinking

rather

than

dissecting

tasks

among group members

In addition we designed this activity to depend on analysis of

data, evaluation of results, and extension of concepts of a real-life

chemistry application.

Activity

The same principles and rationale apply to the two ex

-

amples provided: self-heating beverage and MRE (or the FRH

system). Instructors may use the example that students are more

familiar with so that chemistry principles become more tangible

to them. The aim is to propose a real-life chemistry problem for

which students will need to calculate the heat produced by the

chemical reaction or the dissolution process, the accompany

-

ing theoretical change in temperature, and finally compare the

theoretical change to the temperature observed. With either

methodolog y, PBL or IGI, the instructor shows the class the

container, carries out a demonstration, and gives necessary data

or appropriate information resources. The activity is designed

to use five minutes of class time and allow students to work in

groups, outside the classroom, to solve the problem posed.

Self-Heating Beverage

In class, the instructor asks a student to follow the direc

-

tions on the label of the self-heating chocolate beverage, while

the instructor does the demonstration. The temperature reached

inside the beverage container is recorded. The beverage is passed

around the classroom for students to feel the warmed container.

Students are given the masses of the different substances. In this

particular example these are CaCl

2

(54.31

g ), water (60.45

g ),

chocolate (93.68

g and a volume of 75 mL), container (21.22 g

polypropylene and 8.39

g Al). The instructor may choose to

adopt PBL methodolog y when presenting this activity to the

students and the problem could be similar to the one presented

in Figure 1. If the methodolog y adopted is IGI, a homework

set may be distributed that includes the following guiding

questions:

a)

Draw a scheme that describes the container (materials

and design). Based on this design could you propose the

chemical process involved in heating the beverage?

b)

Suggest a procedure by which the instructor was able to

determine the masses given.

c)

Because the dissolution of CaCl

2

in water is an exother

-

mic process, how would you estimate the heat (in kJ)

liberated during the process and the temperature the

beverage should reach? Does the estimated temperature

match the temperature claimed by the manufacturer of

the container? Provide explanations and state possible

assumptions.

d)

Explain the rationale for the following recommendations

given in the product label:

i) Shake upside down for 40 seconds.

ii) Do not perforate or cut the container.

iii) Self-heating will occur only once.

iv) Do not warm the container by any other means such

as microwave or oven.

e)

Comment on the advantages or disadvantages of this type

of container and suggest improvements.

f )

Decide whether this type of container could be used to

cool a beverage rather than to heat it. Propose a chemical

process that could achieve that.

g )

With the data provided in this exercise, could you

compute the density of the chocolate? Using values of

the enthalpy of salt dissolution in water and other ther

-

mochemical data, could you calculate the lattice energ y

of the salt?

The proposed solutions to each question can be found in the

online material.

It is worth pointing out the rationale for including each of

these questions in the homework is because the methodolog y

is as important as the exercise. When students are required to

examine the information provided by manufacturers they realize

that without a chemical equation to describe the process they

Figure

1. Scheme

of the self-heating

beverage container and PBL problem.

Product A:

Self-Heating Beverage

PBL Problem:

Currently there are commercial

products that claim to heat its contents

based on the dissolution process of

a salt, in our case, calcium chloride.

We need to warm the 76 mL of the

beverage in this container to 60 °C.

To do so we need to know how much

salt and water are required in this

container.