Lab 4 - Calorimetry

Purpose

To determine if a Styrofoam cup calorimeter provides adequate insulation for heat transfer measurements, to identify an unknown metal by means of its heat capacity and to determine a heat of neutralization and a heat of solution.

Goals

• 1
  To perform simple calorimetry experiments.
• 2
  To use calorimetry results to calculate the specific heat of an unknown metal.
• 3
  To determine heat of reaction (ΔH) from calorimetry measurements.

Introduction

Heat and work are the two most common ways for a system to exchange energy with its surroundings. The work term in reactions that do not involve gases is zero, so all of the energy change results in heat. The amount of heat that flows into or out of the surroundings is determined with a technique called calorimetry (heat measurement). A calorimeter is composed of an insulated container, a thermometer, a mass of water, and the system to be studied. The use of an insulated container (Styrofoam cup in this experiment) allows us to assume that there is no heat transferred through the calorimeter walls. In other words, we can assume that the thermodynamic universe is composed of the system and the surrounding water. In the experiment, we will test this assumption. All of the heat absorbed or given off by a system (q_sys) is exchanged with its surroundings (q_sur), which is expressed mathematically in equation 1.

( 1 )

q_sys = −q_sur 

Remember that q > 0 means that the heat flows into the system, while q < 0 means that heat flows out of the system. The minus sign in equation 1 simply implies that the heat flows in opposite directions relative to the system and its surroundings. That is, any heat that flows out of a reaction must flow into the surroundings, and vice versa. In this experiment, water serves as the surroundings. We assume that no heat is exchanged through the walls of the insulated container, and we write the following:

( 2 )

q_sur = q_water 

The heat that is exchanged with the water causes a temperature change of ΔT_water in the water as shown in equation 3.

( 3 )

q_water = C_water· ΔT_water 

where C_water is the heat capacity of the water, the amount of heat needed to raise the temperature of the water by 1°C. The units of C are J/°C. ΔT is the temperature change, defined as ΔT = T_final - T_initial. Heat capacities depend upon the mass of the sample, so the specific heat, the amount of heat needed to raise the temperature of one gram of a substance by 1°C, is often used instead. The symbol for specific heat is s. The specific heat of water is 4.18 J/g · °C. The heat capacity of the water equals the mass of water times the specific heat of water, i.e., C_water = m_water · s_water. Substitution into equation 3 yields equation 4:

( 4 )

q_water = m_water · s_water · ΔT_water 

Finally, equations 1, 2 and 3 can be combined into the calorimetry equation:

( 5 )

q_sys = -q_water = -m_water·s_water·ΔT_water = -m_water·(4.18 J/g·°C)·ΔT_water

 

In the preceding discussion, we have assumed that all of the heat transfer involves the water in the calorimeter, and that the calorimeter apparatus (the Styrofoam cup, the air inside, the thermometer, etc.) is not involved in the heat transfer. We will test the validity of this assumption to convince ourselves that the data we get from subsequent calorimetry experiments is reliable. This test will be conducted in Part A of this lab. Warm water will be added to cold water in the calorimeter. If we designate the warm water as the system, we can write:

( 6 )

m_{warm water} s_{warm water} ΔT_{warm water} = −m_{cold water} s_{cold water} ΔT_{cold water}

 

The mass and temperature change of both the warm and cold water will be measured. If our assumption that the calorimeter apparatus is not involved in the heat transfer is correct, then the two sides of the equation should be equal. The extent to which they vary from equality will give an estimate of the validity of the assumption. In Part B of this lab, the system is an unknown metal, and we can write:

( 7 )

m_metal s_metal ΔT_metal = −m_water s_water ΔT_water

 

The masses of water and metal, and the temperature changes they undergo, will be measured. With these values, the specific heat of the metal can be calculated. A table of specific heats of metals is included in this experiment to allow you to identify the metal. In reactions carried out at constant pressure, the heat that is absorbed or given off is called the heat or enthalpy of reaction (ΔH). The enthalpy of reaction is the result of the difference in potential energies of the reactants and the products. The sign of ΔH specifies the direction of heat flow. If ΔH < 0 (the potential energy of the reactants is greater than that of the products), heat is given off and the reaction is exothermic. If ΔH > 0 (the potential energy of the reactants is less than that of the products), heat is absorbed and the reaction is endothermic. In Part C of the lab, the system is an acid/base "neutralization" reaction.

( 8 )

NH₃(aq) + H₃PO₄(aq) NH₄⁺(aq) + H₂PO₄^-(aq)

 

In Part D of the lab, the system is the dissolution of a salt.

( 9 )

NH₄H₂PO₄(s) NH₄⁺(aq) + H₂PO₄^-(aq)

 

Since these systems are reactions,

( 10 )

ΔH = -m_water s_water ΔT_water

 

The ΔH obtained for Reaction 8 is called the "heat of neutralization", while that determined for Reaction 9 is called the "heat of solution". Technically, this acid/base reaction is not a neutralization, since the products are not a salt and water, but rather a weak acid and a weak base. Note that the terms "enthalpy" and "heat" are synonymous, and chemists use the two interchangeably. Thus, "heat of reaction" and "enthalpy of reaction" mean the same thing. Enthalpy changes for reactions depend on the amounts of reactants used; consider the difference between blowing up a speck of dynamite and a stick of dynamite! In order to compare the energetics of different reactions, ΔH data from calorimetry is usually converted to "molar enthalpies," the ΔH that would be measured if the reaction were run on a one mole scale. Analysis of the units in the calorimetry equations above shows that ΔH is in Joules. Conversion to molar enthalpy requires determining the number of moles of a compound that have reacted. For example, if 500 J of heat were produced when 0.20 moles of compound dissolved, the molar enthalpy would be:

( 11 )

500 J

0.20 mol

= 2,500

J

mol

or 2.5 kJ/mol

 

In Part A of this experiment, you will check the assumption that the Styrofoam cup calorimeter insulates the system (reaction of interest) and surroundings (water) well enough to make reliable heat transfer measurements. In Part B, you will identify an unknown metal by measuring its specific heat and comparing the result to values for metals of known identity. In Part C, you will measure the heat of neutralization for the reaction of phosphoric acid and ammonia. In part D, you will measure the heat of solution of ammonium phosphate.

Equipment

Reagents

Safety

Phosphoric acid is corrosive. It can attack the skin, cause permanent damage to the eyes, and cause burns. If contact with skin or clothing occurs, immediately rinse the affected area with water for at least 15 minutes and have your lab partner notify the teaching assistant. Do not inhale the fumes. If you inhale enough ammonia vapors to cause discomfort, get to fresh air. Have your lab partner notify the teaching assistant of the problem. Students will have access to gloves owing to the use of concentrated acid and base solutions during the lab period.

Waste Disposal

All solutions may be disposed of down the sink drain followed by flushing with plenty of water. Do not put the metal samples in the sink. Return them to the side shelf in the appropriate containers.

Prior to Class

Please review the following video:

• Safety

Please complete WebAssign prelab assignment. Check your WebAssign Account for due dates. Students who do not complete the WebAssign prelab are required to bring and hand in the prelab worksheet.

Lab Procedure

Please print the worksheet for this lab. You will need this sheet to record your data.

Part A: Validating the Assumption about Insulation

Part B: Identifying an Unknown Metal by Specific Heat

Part C: Heat of Neutralization

Part D: Heat of Solution

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