Lab 3 - Heats of Transition, Heats of Reaction, Specific Heats, and Hess's Law

Goal and Overview

A simple calorimeter will be made and calibrated. It will be used to determine the heat of fusion of ice, the specific heat of metals, and the heat of several chemical reactions. These heats of reaction will be used with Hess's law to determine another desired heat of reaction.

Objectives of the Data Analysis

• •
  understand calorimetry and the concepts and uses of heat transfer
• •
  understand heat transfer processes
• •
  understand a variety of heat-related topics, including specific heat and heat capacity, heat of fusion, and heat of a chemical reaction
• •
  use Hess's Law to deduce an unknown heat of reaction

Suggested Review and External Reading

• •
  See reference section; textbook information on calorimetry and thermochemistry

Background

The internal energy, E, of a system is not always a convenient property to work with when studying processes occurring at constant pressure. This would include many biological processes and chemical reactions done in lab. A more convenient property is the sum of the internal energy and pressure-volume work

(−w_sys = PΔV

at constant P). This is called the enthalpy of the system and is given the symbol H. Enthalpy is simply a corrected energy that reflects the change in energy of the system while it is allowed to expand or contract against a constant pressure. For any process occurring at constant pressure, the change in the enthalpy, ΔH, is the heat absorbed or released by the system. A system can be thought to "contain" enthalpy, just as it does energy. Some contributions to the enthalpy of a system include the following.

• 1
  Thermal Enthalpy. The higher the system's temperature, the greater its enthalpy. This makes sense because it takes heat to raise the temperature of an object.
• 2
  Phase Enthalpy. The liquid phase has higher enthalpy than the solid, and the vapor phase has higher enthalpy than the liquid. This also makes sense because it takes heat to melt a solid or to vaporize a liquid.
• 3
  Chemical Enthalpy. Chemical bonds store energy. When a chemical reaction occurs, the chemical enthalpy of the reactants changes when they form products.
  • i
    If the reaction is exothermic, the chemical enthalpy decreases as the reaction proceeds.
  • ii
    If the reaction is endothermic, the chemical enthalpy increases as the reaction proceeds.

Enthalpy changes are determined by measuring the amount of heat transferred during a physical or chemical process. The quantitative treatment of the above three kinds of enthalpy, are all based on use of Eq. 2

ΔH ≡ H_final − H_initial = q_p = heat absorbed by system     (constant p)

 

.

Temperature

When there is a change in the temperature of the system, ΔH is proportional to the temperature change,

T_final − T_initial = ΔT. 

The proportionality constant is called the heat capacity, and is given the symbol C. Because it is the difference in temperature that determines ΔH, either °C or K temperatures will give the identical result. ΔH of the system is also proportional to the amount of material. The heat energy required to raise the temperature of one gram of material is its specific heat capacity, c. If amount is expressed in moles, then the molar heat capacity C is used. Therefore, the system's ΔH is the product of the amount, the heat capacity (specific or molar), and the change in temperature. If ΔT of the system is positive, temperature increases, the system absorbs heat, and q (or ΔH) is positive. If ΔT of the system is negative, temperature decreases, the system gives off heat to its surroundings, and q (or ΔH) is negative. Unit analysis will help you determine how to use the above equation. ΔH (or q) must have an energy unit. Units for heat capacity are:

Phase

At a phase change, the temperature of the system is constant until the transition is complete. The amount of heat required is proportional to the amount or material present, and the ΔH of the phase transition. The heat energy can also be expressed in terms of moles (heat per mole). The value of ΔH is positive (heat is absorbed) for melting, vaporization, and sublimation processes. It is negative for the reverse (freezing, condensation, and deposition). In this experiment, we will use 'Δh' to represent the enthalpy change per gram.

Chemical Reaction

The chemical reactions studied here occur at a particular pressure and temperature. Each reaction has an associated enthalpy change that is called the heat or enthalpy of reaction that depends on the way the reaction is balanced. For example,

ΔH_reaction

for

2 H₂O → 2 H₂ + O₂

is twice that for

H₂O → H₂ + ¹/₂ O₂, and ΔH_reaction

is the heat absorbed when 2 moles of water decompose to give two moles of hydrogen and one mole of oxygen. In general, the equation to calculate the heat change is similar to Eq. 5

ΔH = m Δh_{per gram} = n ΔH_{per mole}     (phase change) 

.

Calorimeter

A calorimeter is an insulated vessel in which physical or chemical processes are performed while neglecting heat flow between the vessel and its surroundings. A process in which the heat flow, q, equals zero is called adiabatic. To a first approximation, the heat flow (+ or –) between calorimeter and the surroundings is zero, so ΔH (or q) for the calorimeter and its contents will be zero.

Example 1: Calorimeter Calibration

A mass m₁ of water at temperature T₁ is placed in the calorimeter. Mass m₂ of water at T₂ is added. The calorimeter itself has a small heat capacity that must be accounted for in order to have reasonable precision. The calorimeter always contributes a term to the total enthalpy change. Initially, the calorimeter is at the same temperature, T₁, as the water it contains. When heat flow stops, all of the water and the calorimeter have reached the same temperature T_final (at thermal equilibrium). In this example, there are three quantities contributing to the total enthalpy change (which is assumed to be zero): the two amounts of water and the calorimeter. Note that the initial temperatures are not the same, but everything shares a common final temperature. Eq. 5

ΔH = m Δh_{per gram} = n ΔH_{per mole}     (phase change) 

was used for ΔH₁ and ΔH₂. Generally all but one quantity in calculations like that shown in Eqns 9a

ΔH_total = 0 

, 9b

ΔH₁ + ΔH_calorimeter + ΔH₂ = 0 

, and 9c

m₁c_water(T_final − T₁) + C_calorimeter(T_final − T₁) + m₂c_water(T_final − T₂) = 0 

are measured or known. The equation is then solved for the unknown value.

Example 2: Specific Heat Determination

Suppose a mass m₁ of water with specific heat c₁ is placed in the calorimeter at T₁. Then a mass m₂ of another substance, such as a metal, at T₂ and with specific heat c₂ is added. The equation is similar to that of Eqns 9a

ΔH_total = 0 

, 9b

ΔH₁ + ΔH_calorimeter + ΔH₂ = 0 

, and 9c

m₁c_water(T_final − T₁) + C_calorimeter(T_final − T₁) + m₂c_water(T_final − T₂) = 0 

except that the 'c's do not cancel in the last step. Note again that the initial temperatures are not the same, but everything shares a common final temperature. Eq. 5

ΔH = m Δh_{per gram} = n ΔH_{per mole}     (phase change) 

was used for ΔH₁ and ΔH₂. Again, usually all but one quantity are measured or known. The equation is then solved for the unknown value. In 1819, after analyzing the heat capacities of many solid elements, Dulong and Petit proposed this generalization known as the Law of Dulong and Petit: Using precise specific heat measurements, Berzelius used Eq. 11 to find many molar masses. In 1830, he published an extremely accurate table of molar masses that gave great impetus to the development of atomic/molecular theory.

Example 3: Enthalpy of Phase Change Determination

Suppose a mass m₁ of water is placed in the calorimeter at T₁, and mass m₂ of ice at 0°C is added. As the apparatus reaches thermal equilibrium, several things occur. First, the ice melts, pulling its heat of fusion out of the thermal energy of the water and calorimeter, thus lowering their temperatures. Second, when the ice has melted, the resulting liquid is still at 0°C, so that water has to be further heated until it, the water it is cooling, and the calorimeter reach the same final temperature. Note that the heat of fusion of ice is expressed in units of energy per mass (J/g or kJ/g); if the amount of ice were in moles, the heat of fusion would have units of energy per mole (J/mol or kJ/mol).

Example 4: Reaction Enthalpy Determinations

Suppose mass m₁ of a water-based solution is placed in the calorimeter at T₁. To that mass m₂ of a substance of molar mass M₂ is added and it reacts with the solution. If substance 2 is the limiting reactant, then all of it will react. The enthalpy change will depend on the heat of reaction and on the number of moles of substance 2 added, n₂ = m₂/MM₂. In this case, there are three contributions to the total enthalpy change of zero. They are due to the temperature change of the water solution and calorimeter, plus the enthalpy change due to the chemical reaction. For reactions in solution, the heat capacities of the reactants and products are approximated as zero because only the water and the calorimeter have significant heat capacity. In the last step it is assumed that the chemical reaction is written in such a way that the stoichiometric coefficient on the reactant, substance 2, is 1. The last term has been written so that ΔH_reaction has a unit of energy per mole (J/mol or kJ/mol). In 1840, Hess stated that the evolution of heat by chemical reactions is the same, regardless of whether the reaction takes place in one step or in more than one. Heats of reaction are changes in the property, H, of a system. When a system changes from state 1 to state 2, H will have to change by the amount H₂ – H₁, regardless of the number or kind of steps involved in the process. Hess' Law permits the heats of experimentally difficult reactions to be deduced from measurements of other more convenient reactions.

Experimental Notes

There are two possibilities for your calorimeter setup, but both require the same procedure.

• a
  Coffee Cup Calorimeter Setup — the calorimeter consists of two nested Styrofoam cups with a lid.
• b
  Styrofoam Calorimeter Setup — the calorimeter consists of a Styrofoam base and lid.

A thermometer is placed through a hole in the lid to measure the temperature of the liquid. If you use set-up (a), use a slotted rubber stopper to protect the thermometer in the clamp. Both setups are constant pressure calorimeters.

Measurements

The two key measurements for all calorimetry experiments are masses and temperature changes. Make sure you have all of the data you need to complete the lab. You may need these conversion factors: 1000 J = 1 kJ, and 4.184 J = 1 cal.

Procedure

Part 1: Heat Capacity of the Calorimeter

This is the experiment discussed in Example 1. This result is important because you will use it in the other experiments you perform with this calorimeter.

• Finding the heat capacity of your calorimeter this way is very sensitive to small errors. The "correct" value is probably between 5 and 150 J/°C. If you get a negative value or a very large value, re-do the calculation or the experiment. Use a new set of cups if you get a high calorimeter constant (heat loss).

Part 2: Heat of Fusion of Ice

This is the experiment discussed in Example 3.

Part 3: Specific Heat of a Metal

Begin the temperature equilibration of the metal at the beginning of the lab. This is the experiment given in Example 2.

Part 4: Heat of a Chemical Reaction

This experiment is discussed in Example 4. You will measure the heats of two reactions:

• a
  Mg + 2 HCl → MgCl₂ + H₂(g)      ΔH_a = measured 
• b
  MgO + 2 HCl → MgCl₂ + H₂O(l)      ΔH_b = measured 

You also need a ΔH value for reaction c, which is from the literature.

• c
  H₂(g) + ¹/₂ O₂(g) → H₂O(l)      ΔH_c = −285.8 kJ 

Using these ΔH values and Hess's Law, you can determine the ΔH for magnesium combustion (or formation), where magnesium metal is burned in oxygen.

• d
  Mg + ¹/₂ O₂ → MgO      ΔH_d = ??? 

Waste Disposal: As per TA instruction; you will lose points if you do not dispose of waste properly.

Reporting Results

Complete your lab summary or write a report (as instructed).

Abstract

Results (final results are reported to three significant figures)

• Calorimeter heat capacity
• Heat of fusion of ice
• Specific heats of metals
• Heats of reaction from part 4 and for combustion of Mg.

Sample Calculations

• Calorimeter heat capacity (part 1)
• Heat of fusion of ice (part 2)
• Specific heat of metals (part 3)
• Heat of reaction for one of part 4 reactions (part 4)
• Heat of magnesium combustion using Hess' Law (part 4)

Discussion

• What you found out and how for each part
• How good was your data (comparison to expected values, etc.)
• Ideas to improve the accuracy in any or all of the procedures utilized in this experiment?
• What conclusions can you draw?

Review

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