Calorimetry And Hess's Law Pre Lab Answers

Calorimetry and Hess's Law are fundamental concepts in thermochemistry, the study of heat and energy associated with chemical reactions and physical transformations. Understanding these principles is crucial for determining the enthalpy changes that occur during various processes, allowing us to predict the feasibility and energy requirements of chemical reactions. Before diving into a laboratory experiment exploring these concepts, let's review the underlying theory, calculations, and potential pitfalls.

Calorimetry: Measuring Heat Flow

Calorimetry is the experimental technique used to measure the heat exchanged during a chemical reaction or physical change. The core principle rests on the law of conservation of energy: energy cannot be created or destroyed, only transferred. In a calorimeter, the heat released or absorbed by the reaction (or process) is transferred to the calorimeter itself, and by carefully measuring the temperature change of the calorimeter, we can determine the amount of heat involved.

Types of Calorimeters

• Coffee-Cup Calorimeter (Constant Pressure Calorimetry): This simple calorimeter consists of two nested Styrofoam cups, a lid, and a thermometer. It operates at constant atmospheric pressure and is ideal for measuring the heat of solution, heat of neutralization, and other reactions in solution.
• Bomb Calorimeter (Constant Volume Calorimetry): A bomb calorimeter is a more sophisticated device used to measure the heat of combustion reactions. It consists of a sealed, rigid metal container (the "bomb") where the reaction takes place, surrounded by a water bath. Because the volume is constant, no work is done, and the heat released directly corresponds to the change in internal energy.

Key Equations in Calorimetry

The fundamental equation in calorimetry relates the heat transferred (q) to the temperature change (ΔT), the mass of the substance (m), and its specific heat capacity (c):

q = mcΔT

Where:

• q is the heat absorbed or released (in Joules or calories)
• m is the mass of the substance (in grams)
• c is the specific heat capacity (in J/g°C or cal/g°C) – the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius.
• ΔT is the change in temperature (in °C), calculated as T_final - T_initial.

For bomb calorimeters, we use a slightly different approach:

q = CΔT

Where:

• q is the heat absorbed or released (in Joules or calories)
• C is the heat capacity of the calorimeter (in J/°C or cal/°C) – the amount of heat required to raise the temperature of the entire calorimeter by 1 degree Celsius.
• ΔT is the change in temperature (in °C).

Determining the Heat Capacity of a Calorimeter

Before using a calorimeter, its heat capacity (C) must be determined experimentally. This involves introducing a known amount of heat into the calorimeter (often by adding a known mass of hot water) and measuring the resulting temperature change. The heat capacity can then be calculated using the following equation:

C = q / ΔT

Where q is the known heat added to the calorimeter.

Calculating Enthalpy Change (ΔH)

Calorimetry experiments allow us to determine the heat transferred (q) at constant pressure (using a coffee-cup calorimeter) or constant volume (using a bomb calorimeter). However, chemists are usually more interested in the enthalpy change (ΔH), which represents the heat absorbed or released at constant pressure.

For reactions carried out in a coffee-cup calorimeter at constant pressure, the enthalpy change (ΔH) is equal to the heat transferred (q):

ΔH = q

For reactions carried out in a bomb calorimeter at constant volume, the heat transferred (q) is equal to the change in internal energy (ΔU). The enthalpy change (ΔH) can then be calculated using the following equation:

ΔH = ΔU + PΔV

Where:

• P is the pressure
• ΔV is the change in volume

For reactions involving only solids and liquids, the change in volume is typically negligible, so ΔH ≈ ΔU. However, for reactions involving gases, the ΔV term can be significant and must be taken into account.

Hess's Law: Adding Enthalpy Changes

Hess's Law states that the enthalpy change for a reaction is independent of the pathway taken. In other words, if a reaction can be carried out in one step or a series of steps, the total enthalpy change will be the same. This law is a direct consequence of enthalpy being a state function – its value depends only on the initial and final states, not on the path taken to get there.

Applications of Hess's Law

Hess's Law is incredibly useful for calculating enthalpy changes for reactions that are difficult or impossible to measure directly. By manipulating known enthalpy changes for other reactions, we can determine the enthalpy change for the target reaction.

To apply Hess's Law, you can use the following rules:

1. If a reaction is reversed, the sign of ΔH is reversed. This is because reversing a reaction changes the direction of heat flow.
2. If a reaction is multiplied by a coefficient, the value of ΔH is multiplied by the same coefficient. This is because enthalpy is an extensive property, meaning it depends on the amount of substance.
3. Reactions can be added together to obtain a new reaction, and the ΔH values for these reactions can be added together to obtain the ΔH for the new reaction. This is the heart of Hess's Law.

Calculating Enthalpy Changes Using Standard Enthalpies of Formation

A particularly useful application of Hess's Law involves using standard enthalpies of formation (ΔH_f°). The standard enthalpy of formation of a compound is the enthalpy change when one mole of the compound is formed from its elements in their standard states (usually 298 K and 1 atm). Standard enthalpies of formation are typically tabulated in reference books and online databases.

The enthalpy change for a reaction can be calculated using the following equation:

ΔH°<sub>reaction</sub> = ΣnΔH°<sub>f</sub>(products) - ΣnΔH°<sub>f</sub>(reactants)

Where:

• ΔH°_reaction is the standard enthalpy change for the reaction.
• ΔH°_f(products) is the standard enthalpy of formation of each product.
• ΔH°_f(reactants) is the standard enthalpy of formation of each reactant.
• n is the stoichiometric coefficient for each product and reactant in the balanced chemical equation.

Important Note: The standard enthalpy of formation of an element in its standard state is defined as zero.

Pre-Lab Questions: Applying the Concepts

Now, let's tackle some common pre-lab questions related to calorimetry and Hess's Law:

Question 1: A 50.0 mL sample of 1.0 M HCl is mixed with 50.0 mL of 1.0 M NaOH in a coffee-cup calorimeter. The initial temperature of both solutions is 22.0 °C. After mixing, the temperature rises to 28.7 °C. Assuming the density of the solution is 1.00 g/mL and the specific heat capacity is 4.184 J/g°C, calculate the enthalpy change for the neutralization reaction (in kJ/mol of HCl).

Solution:

1. Calculate the total mass of the solution:

   Total volume = 50.0 mL + 50.0 mL = 100.0 mL

   Total mass = Volume x Density = 100.0 mL x 1.00 g/mL = 100.0 g

2. Calculate the temperature change:

   ΔT = T_final - T_initial = 28.7 °C - 22.0 °C = 6.7 °C

3. Calculate the heat absorbed by the solution (q):

   q = mcΔT = (100.0 g) x (4.184 J/g°C) x (6.7 °C) = 2803.28 J = 2.803 kJ

4. Determine the moles of HCl reacted:

   Moles of HCl = Volume x Molarity = 0.050 L x 1.0 mol/L = 0.050 mol

5. Calculate the enthalpy change per mole of HCl:

   ΔH = -q / moles of HCl = -2.803 kJ / 0.050 mol = -56.06 kJ/mol

   Therefore, the enthalpy change for the neutralization reaction is -56.06 kJ/mol. The negative sign indicates that the reaction is exothermic.

Question 2: The heat capacity of a bomb calorimeter is determined by burning 0.855 g of benzoic acid (C₇H₆O₂) in excess oxygen. The temperature of the calorimeter increases from 21.84 °C to 26.42 °C. The heat of combustion of benzoic acid is -26.42 kJ/g. Calculate the heat capacity of the calorimeter.

Solution:

1. Calculate the total heat released by the combustion of benzoic acid:

   q = mass of benzoic acid x heat of combustion = 0.855 g x (-26.42 kJ/g) = -22.58 kJ

2. Calculate the temperature change:

   ΔT = T_final - T_initial = 26.42 °C - 21.84 °C = 4.58 °C

3. Calculate the heat capacity of the calorimeter:

   C = q / ΔT = 22.58 kJ / 4.58 °C = 4.93 kJ/°C

   Therefore, the heat capacity of the calorimeter is 4.93 kJ/°C. Remember to drop the negative sign since heat capacity is always a positive value. We are simply interested in the amount of heat needed to change the temperature.

Question 3: Given the following reactions and enthalpy changes:

N<sub>2</sub>(g) + O<sub>2</sub>(g) → 2NO(g)      ΔH = +180.6 kJ
2NO(g) + O<sub>2</sub>(g) → 2NO<sub>2</sub>(g)     ΔH = -114.1 kJ

Calculate the enthalpy change for the reaction:

N<sub>2</sub>(g) + 2O<sub>2</sub>(g) → 2NO<sub>2</sub>(g)

Solution:

This is a straightforward application of Hess's Law. We can directly add the two given reactions together to obtain the target reaction:

N<sub>2</sub>(g) + O<sub>2</sub>(g) → 2NO(g)      ΔH = +180.6 kJ
2NO(g) + O<sub>2</sub>(g) → 2NO<sub>2</sub>(g)     ΔH = -114.1 kJ
--------------------------------------------------
N<sub>2</sub>(g) + 2O<sub>2</sub>(g) → 2NO<sub>2</sub>(g)     ΔH = +66.5 kJ

Therefore, the enthalpy change for the reaction N₂(g) + 2O₂(g) → 2NO₂(g) is +66.5 kJ.

Question 4: Calculate the standard enthalpy change for the following reaction:

CH<sub>4</sub>(g) + 2O<sub>2</sub>(g) → CO<sub>2</sub>(g) + 2H<sub>2</sub>O(l)

Given the following standard enthalpies of formation:

ΔH°<sub>f</sub>[CH<sub>4</sub>(g)] = -74.8 kJ/mol
ΔH°<sub>f</sub>[CO<sub>2</sub>(g)] = -393.5 kJ/mol
ΔH°<sub>f</sub>[H<sub>2</sub>O(l)] = -285.8 kJ/mol
ΔH°<sub>f</sub>[O<sub>2</sub>(g)] = 0 kJ/mol

Solution:

Using the formula: ΔH°_reaction = ΣnΔH°_f(products) - ΣnΔH°_f(reactants)

ΔH°<sub>reaction</sub> = [1*ΔH°<sub>f</sub>(CO<sub>2</sub>(g)) + 2*ΔH°<sub>f</sub>(H<sub>2</sub>O(l))] - [1*ΔH°<sub>f</sub>(CH<sub>4</sub>(g)) + 2*ΔH°<sub>f</sub>(O<sub>2</sub>(g))]

ΔH°<sub>reaction</sub> = [1*(-393.5 kJ/mol) + 2*(-285.8 kJ/mol)] - [1*(-74.8 kJ/mol) + 2*(0 kJ/mol)]

ΔH°<sub>reaction</sub> = [-393.5 kJ/mol - 571.6 kJ/mol] - [-74.8 kJ/mol]

ΔH°<sub>reaction</sub> = -965.1 kJ/mol + 74.8 kJ/mol = -890.3 kJ/mol

Therefore, the standard enthalpy change for the combustion of methane is -890.3 kJ/mol.

Question 5: The enthalpy of formation of NH₃(g) is -46 kJ/mol. What is the enthalpy change for the reaction:

2NH<sub>3</sub>(g)  ->  N<sub>2</sub>(g)  +  3H<sub>2</sub>(g)

Solution:

The reaction is the reverse of the formation reaction multiplied by 2.

The formation reaction is:

N<sub>2</sub>(g)  +  3H<sub>2</sub>(g)  ->  2NH<sub>3</sub>(g)    ΔH = 2 * (-46 kJ/mol) = -92 kJ/mol

Reversing the reaction changes the sign of ΔH:

2NH<sub>3</sub>(g)  ->  N<sub>2</sub>(g)  +  3H<sub>2</sub>(g)    ΔH = +92 kJ/mol

Therefore, the enthalpy change for the decomposition of 2 moles of ammonia is +92 kJ/mol.

Potential Sources of Error in Calorimetry

Calorimetry, while a powerful technique, is susceptible to several sources of error:

• Heat Loss to the Surroundings: In coffee-cup calorimeters, some heat inevitably escapes to the surroundings, leading to an underestimation of the heat released or absorbed by the reaction. Insulation and careful experimental technique can minimize this error. Bomb calorimeters are much better insulated and minimize this source of error.
• Incomplete Reaction: If the reaction does not proceed to completion, the measured heat change will be less than the theoretical value.
• Heat Absorption by the Calorimeter: The calorimeter itself absorbs some heat, which must be accounted for by determining its heat capacity. Inaccurate determination of the calorimeter's heat capacity will lead to errors in the enthalpy change calculation.
• Non-Ideal Solutions: Assumptions about the density and specific heat capacity of solutions may not be accurate, especially at high concentrations.
• Evaporation: Evaporation of the solvent can absorb heat and affect the temperature measurements.

Conclusion

Calorimetry and Hess's Law are essential tools for understanding and quantifying energy changes in chemical reactions. By carefully applying these principles and understanding potential sources of error, we can accurately determine enthalpy changes and gain valuable insights into the thermodynamics of chemical processes. Thorough preparation, including working through pre-lab questions, is key to a successful and informative laboratory experience. Understanding the underlying theory, equations, and potential pitfalls will allow you to perform experiments with greater confidence and interpret your results with accuracy. Remember to pay close attention to experimental technique and data analysis to minimize errors and obtain reliable results.