Chem1811 Determination of enthalpy changes by calorimetry

Summary

The video explains the thermodynamic principles behind measuring reaction enthalpy by calorimetry, then outlines a lab procedure for measuring the reaction of magnesium with hydrochloric acid. The measured enthalpy is combined with other reaction data using Hess’s law to estimate the enthalpy of formation of magnesium oxide.

Main Concepts

Energy and the First Law

• Energy is the capacity to transfer heat or do work. It can change form but cannot be created or destroyed.
• Energy may be kinetic, associated with motion, or potential, stored in fields or chemical bonds.
• The SI unit of energy is the joule. Other units, such as calories and BTU, can be converted to joules.

Systems and Surroundings

A thermodynamic system is the part of the universe being studied; everything else is its surroundings. A boundary separates them.

• An open system exchanges matter and energy with its surroundings.
• A closed system exchanges energy but not matter.
• An isolated system exchanges neither.

Thermal Energy, Heat, and Calorimetry

• Thermal energy is associated with molecular motion. Heat is thermal energy transferred because of a temperature difference.
• A calorimeter is designed to limit heat exchange with the surroundings and measure a temperature change. Insulation, a thermometer, and mixing help make the measurement useful.
• Heat transfer is related to temperature change by:
  • (q = C\Delta T), where (C) is the heat capacity of the whole system.
  • (q = mc\Delta T), where (c) is specific heat capacity and (m) is mass.
  • (q = nC_m\Delta T), where (C_m) is molar heat capacity.
• In each case, (\Delta T = T_{\text{final}} - T_{\text{initial}}).

Work, Internal Energy, and Enthalpy

• A volume change can involve pressure–volume work. Expansion means work is done by the system; compression means work is done on it.
• Using the sign convention presented, (\Delta U = q - P\Delta V), or equivalently (q = \Delta U + P\Delta V).
• At constant volume, (q_v = \Delta U). At constant pressure, (q_p = \Delta H), where enthalpy is defined as (H = U + PV).
• A positive enthalpy change indicates an endothermic process, in which the system absorbs heat. A negative enthalpy change indicates an exothermic process, in which it releases heat.
• Enthalpy is a state function: its change depends on the starting and ending states, not on the pathway. Reversing a reaction reverses the sign of its enthalpy change.

Hess’s Law and the Target Reaction

Hess’s law says that the enthalpy change for an overall reaction equals the sum of the enthalpy changes for steps that add up to that reaction.

The target reaction is:

[ \mathrm{Mg(s) + \tfrac12 O_2(g) \rightarrow MgO(s)} ]

The lab measures the magnesium–acid reaction:

[ \mathrm{Mg(s) + 2H^+(aq) \rightarrow Mg^{2+}(aq) + H_2(g)} ]

The other supplied reactions are magnesium oxide reacting with acid to form magnesium ions and water, and hydrogen reacting with oxygen to form water. Reverse the magnesium oxide–acid equation so that MgO is a product; reversing it changes the sign of its enthalpy. When the equations are added, common species cancel.

The resulting relationship is:

[ \Delta H_{\mathrm{formation}}(\mathrm{MgO}) = \Delta H_1 - \Delta H_2 + \Delta H_3 ]

The hydrogen–oxygen reaction is not performed in the lab; its supplied enthalpy value is used.

Lab Methodology

1. Prepare and weigh the calorimeter

   • Follow the lab manual’s instructions for preparing the Styrofoam-cup calorimeter and its lid, including the thermometer opening.
   • Weigh the cup with the magnesium ribbon inside, then remove the ribbon and weigh the empty cup. The difference gives the magnesium mass.
   • Avoid touching the cup with bare hands while weighing it. Use gloves, paper, or a lint-free cloth to avoid transferring moisture or heat.

2. Measure the acid

   • Measure 50 mL of 1 M HCl using a measuring cylinder; the instructor notes this introduces some measurement uncertainty.
   • Record the supplied density for the HCl solution and measure its temperature. The acid is intended to be in excess, so magnesium is the limiting reactant.

3. Run the reaction and record temperatures

   • Record the temperature before mixing. At about minute five, lift the lid, add the acid to the magnesium, quickly replace the lid, and note the mixing time.
   • Record the temperature every 30 seconds for roughly seven to eight minutes, gently swirling the cup to mix the contents.
   • Do not use the thermometer as a stirring rod: moving it around can enlarge the lid opening and increase heat loss.

4. Plot the data and estimate (\Delta T)

   • Record readings to one decimal place and plot temperature against time before leaving the lab; have the graph checked as instructed.
   • Choose a broken y-axis that shows the temperature range clearly rather than compressing the data by starting at zero.
   • The temperature may rise to a maximum or plateau and then fall as heat escapes. Do not assume the first reading after mixing is the true final temperature.
   • Draw a tangent through the pre-reaction readings and another through the later post-reaction trend. Extrapolate both to the mixing time; their temperature difference is the corrected (\Delta T).

5. Calculate the reaction enthalpy

   • Use the solution’s mass—not the magnesium mass—in (q = mc\Delta T), because the measured temperature change is that of the solution. Determine solution mass from the measured volume and the supplied density.
   • Account for the direction of heat flow: if the solution warms, it gained heat and the reaction lost it, so (q_{\mathrm{reaction}} = -q_{\mathrm{solution}}). Use the sign consistently when reporting the reaction enthalpy.
   • Divide the reaction heat by the moles of magnesium to obtain the molar enthalpy for reaction 1. Convert to kJ mol(^{-1}) to match the units of the literature values used in Hess’s law.

6. Calculate the internal-energy change

   • For the formation of MgO, the gas-mole change is (\Delta n_{\mathrm{gas}} = 0 - \tfrac12 = -\tfrac12).
   • Use: [ \Delta U = \Delta H - \Delta n_{\mathrm{gas}}RT ] and use (T = 298\ \mathrm{K}) for the standard-temperature literature comparison described in the talk.

Practical Reminders

Bring graph paper and a way to time the reaction. Gloves or another clean way to handle the cup may be useful. Record measurements in pen, avoid spills, and have the graph signed before leaving the lab.

Speakers and Sources

• Speaker: One chemistry instructor/presenter; no other speakers are identified.
• Sources mentioned: The lab manual, thermodynamics material from the course, and supplied literature enthalpy values. No individual authors or additional named sources are identified.