Problem 118 - Chemistry and Chemical Reactivity

Question

In the lab, you plan to carry out a calorimetry experiment to determine \(\Delta_{r} H\) for the exothermic reaction of \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\) and \(\mathrm{HCl}(\mathrm{aq}) .\) Predict how each of the following will affect the calculated value of \(\Delta_{t} H .\) (The value calculated for \(\Delta_{i} H\) for this reaction is a negative value so choose your answer from the following: \(\Delta, H\) will be too low [that is, a larger negative valuel, \(\Delta_{r} H\) will be unaffected, \(\Delta_{r} H\) will be too high [that is, a smaller negative value].) (a) You spill a little bit of the \(\mathrm{Ca}(\mathrm{OH})_{2}\) on the benchtop before adding it to the calorimeter. (b) Because of a miscalculation, you add an excess of HCl to the measured amount of \(\mathrm{Ca}(\mathrm{OH})_{2}\) in the calorimeter. (c) \(\mathrm{Ca}(\mathrm{OH})_{2}\) readily absorbs water from the air. The \(\mathrm{Ca}(\mathrm{OH})_{2}\) sample you weighed had been exposed to the air prior to weighing and had absorbed some water. (d) After weighing out \(\mathrm{Ca}(\mathrm{OH})_{2},\) the sample sat in an open beaker and absorbed water. (e) You delay too long in recording the final temperature. (f) The insulation in your coffee-cup calorimeter was poor, so some energy as heat was lost to the surroundings during the experiment. (g) You have ignored the fact that energy as heat also raised the temperature of the stirrer and the thermometer in your system.

Step-by-Step Solution

Answer

(a) too low, (b) unaffected, (c) too high, (d) too high, (e) too high, (f) too high, (g) too high.

Step 1: Understand the Nature of Reaction

The reaction between \(\text{Ca(OH)}_2\) and \(\text{HCl}\) is exothermic, meaning it releases heat. The calculated enthalpy change \(\Delta_r H\) is negative, indicating energy is released during the reaction. When discussing the effects on \(\Delta_r H\), a value that is "too high" means less negative (closer to zero), while "too low" means more negative.

Step 2: Analyze Effect of Spillage of Reactant

(a) Spilling some \(\text{Ca(OH)}_2\) before the reaction means there is less reactant to undergo the reaction, resulting in less heat being released. Therefore, the calculated \(\Delta_r H\) will be too low, as it would appear that the reaction released more energy per mole than it actually did.

Step 3: Analyze Effect of Excess HCl

(b) Adding excess \(\text{HCl}\) does not change the amount of \(\text{Ca(OH)}_2\) reacting, since \(\text{Ca(OH)}_2\) is the limiting reactant. The reaction proceeds to completion based on the amount of \(\text{Ca(OH)}_2\), hence \(\Delta_r H\) will be unaffected.

Step 4: Effect of Absorbed Water Prior to Weighing

(c) If \(\text{Ca(OH)}_2\) absorbs water, its mass will include water weight. This means the actual \(\text{Ca(OH)}_2\) mass is less than measured, causing calculated \(\Delta_r H\) per mole to be too high—less negative.

Step 5: Effect of Absorbed Water After Weighing

(d) The same reasoning as in Step 4 applies: the additional mass from water makes the effective \(\text{Ca(OH)}_2\) content less than recorded, again making \(\Delta_r H\) appear too high.

Step 6: Delay in Recording Final Temperature

(e) Delaying the recording allows the system to equilibrate with the environment, losing heat. This makes the temperature rise seem less, making \(\Delta_r H\) too high (less negative).

Step 7: Effect of Poor Insulation

(f) Poor insulation allows heat loss to the environment, again causing the measured temperature change to be less than actual, resulting in \(\Delta_r H\) being perceived as too high.

Step 8: Ignoring Heat Absorption by Stirrer and Thermometer

(g) Heat absorbed by the stirrer and thermometer is not accounted for in calorimeter results, leading to an apparent smaller temperature rise and making \(\Delta_r H\) seem too high.

Key Concepts

Enthalpy Change

In the context of a chemical reaction, enthalpy change (\(\Delta_r H\)) is a critical measure. It represents the total energy change when reactants are transformed into products. This change signifies whether a reaction absorbs or releases heat, often presented in kilojoules per mole (kJ/mol). For exothermic reactions, like the one between \(\text{Ca(OH)}_2\) and \(\text{HCl}\), \(\Delta_r H\) is negative because heat is released.

To understand enthalpy change in a calorimetry experiment, it's important to accurately measure the heat exchange within an isolated system. Any errors, such as not considering heat absorbed by apparatus or reactant inconsumption, affect the accuracy, either increasing or decreasing the calculated \(\Delta_r H\). In instances where the energy change is lower than actual (more negative), it might seem that more heat was generated per mole than reality. Conversely, if the calculated value is less negative (closer to zero), it indicates an underestimation of heat released.

Exothermic Reaction

An exothermic reaction is one in which energy is released to the surroundings in the form of heat. When performing a calorimetry experiment involving the exothermic reaction between \(\text{Ca(OH)}_2\) and \(\text{HCl}\), understanding this heat release is essential.

Key characteristics of exothermic reactions include:

• Enthalpy (\(\Delta_r H\)) is always negative, signifying a net loss of energy during the reaction.
• Temperature of the surroundings increases because the system releases heat.

It's crucial in a laboratory setting to note that any deviation in experimental conditions, like incomplete reaction or insulation inefficacy, can alter the perceived heat release, leading to incorrect evaluations of the reaction's enthalpy change.

Heat Capacity

Heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius. In calorimetry, this concept is fundamental as it dictates how substances used in the experiment absorb and exchange heat. A calorimeter itself, including the contained solution, possesses a certain heat capacity.

Understanding the heat capacity of materials is critical for deriving accurate results in calorimetry:

• If the calorimeter's heat capacity is known, the experimenter can accurately account for the heat absorbed by the apparatus instead of just the solution.
• Failure to consider heat capacity may lead to errors, inaccurately attributing the absorbed heat to the chemical reaction itself.

Recognizing how heat travels through different components of the system can thus help in obtaining precise measurements of enthalpy change.

Experimental Error in Calorimetry

Experimental error is an integral part of any scientific endeavor and can significantly impact calorimetry results. Several factors can contribute to these errors, particularly affecting the calculated enthalpy change (\(\Delta_r H\)) of reactions.

Some common sources of error include:

• Spillage of reactants, which alters the quantity available for the reaction, leading to miscalculated heat release.
• Heat absorption by parts of the calorimeter like stirrers or thermometers, not initially accounted for in calculations, leaving you with altered heat data.
• Inadequate calorimeter insulation means loss of energy to the environment, affecting the measured temperature change.
• Delayed measurement of temperatures can lead again to incorrect conclusions about the heat exchange.

Addressing these potential errors involves using better insulation, accurately measuring and accounting for all variables, and ensuring the reaction proceeds under controlled conditions.