Find H for the combustion of ethanol (C2H6O) to carbon dioxide and liquid water from the following data. The heat capacity of the bomb calorimeter is 34.65 kJ/K, and the combustion of 1.765 g of ethanol raises the temperature of the calorimeter from 294.33 K to 295.84 K.

Short Answer

Expert verified
The molar heat of combustion of ethanol (\(\Delta H_{combustion}\text) is found by calculating the temperature change, the total heat absorbed, the heat per gram of ethanol, and then converting it to molar heat using ethanol's molar mass.

Step by step solution

01

Determine the temperature change

Calculate the change in temperature (\Delta T\text) that results from the combustion of ethanol. \[ \Delta T = T_{final} - T_{initial} \] where \[ T_{final} = 295.84 \, K \] and \[ T_{initial} = 294.33 \, K \].
02

Calculate heat absorbed by the calorimeter

Use the temperature change to calculate the heat absorbed by the calorimeter, utilizing its heat capacity (C). \[ q = C \times \Delta T \] where \[ C = 34.65 \, kJ/K \].
03

Calculate the heat of combustion per gram of ethanol

The heat of combustion per gram of ethanol (q_{per gram}) is calculated by dividing the total heat absorbed by the calorimeter by the mass of ethanol combusted. \[ q_{per \, gram} = \frac{q}{m_{ethanol}} \] where \[ m_{ethanol} = 1.765 \, g \].
04

Find the molar heat of combustion of ethanol

To find the molar heat of combustion (\(\Delta H_{combustion}\)), multiply the heat of combustion per gram by the molar mass of ethanol (M). The molar mass of ethanol (C2H6O) is \[ M = 2 \times 12.01 \, g/mol \, (for \, Carbon) + 6 \times 1.008 \, g/mol \, (for \, Hydrogen) + 1 \times 16.00 \, g/mol \, (for \, Oxygen) = 46.07 \, g/mol \]. \[ \Delta H_{combustion} = q_{per \, gram} \times M \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calorimetry
Calorimetry is an experimental technique used to measure the amount of heat released or absorbed during a chemical reaction, phase transition, or some other physical process. Simple calorimeters consist of a container, usually filled with water, where the reaction takes place, which is insulated to minimize heat loss. Thermometers or temperature sensors monitor the system’s temperature change, which is then used to calculate the energy change in the reaction.

To determine the heat involved in a chemical reaction, one measures the temperature change of the water and uses the specific heat capacity of the water to calculate the energy transferred. Calorimetry is essential because it allows scientists to measure enthalpy changes, a critical aspect of understanding thermodynamic and kinetic phenomena in chemistry.
Enthalpy Change
Enthalpy change (abla H) is a critical concept in chemical thermodynamics, representing the heat absorbed or released by a system at constant pressure. It's also known as the heat of reaction for a given process. Essentially, it's the difference in the total enthalpy of the products and the total enthalpy of the reactants.

The enthalpy change can be either exothermic (negative abla H, releases heat) or endothermic (positive abla H, absorbs heat). This property is crucial for scientists and engineers to determine the amount of energy required for a reaction or released during the reaction, which is particularly relevant in processes involving heat exchange, such as combustion.
Bomb Calorimeter
A bomb calorimeter, a type of constant-volume calorimeter, is a device used for measuring the heat of combustion of a particular reaction. Inside a strong metal container, the reaction takes place in an oxygen-rich environment, ensuring it goes to completion without losing any reactants or products beyond the sealed chamber.

Operation of a Bomb Calorimeter

The sample is placed in the bomb, which is then filled with oxygen at high pressure. The bomb is immersed in a water container with a known volume and heat capacity. After igniting the sample, one measures the temperature change of the water, to calculate the energy released by the reaction. This procedure directly relates to the concept of enthalpy change, as it measures the total heat given off in a combustion reaction.
Chemical Thermodynamics
Chemical thermodynamics is a branch of thermodynamics that deals with energy changes, particularly the exchange of heat and the work done in chemical reactions and phase changes. The laws of thermodynamics govern how processes are conducted and whether they can happen spontaneously, based on concepts like entropy and enthalpy.

Understanding chemical thermodynamics is crucial for grasping how different forms of energy transformations can be harnessed or controlled. It allows chemists to predict the behavior of reactions under various conditions, to calculate system properties like the Gibbs free energy, and to understand the energy profiles of reactions and how they can be optimized for various applications.

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Most popular questions from this chapter

A person packs two identical coolers for a picnic, placing twenty-four 12-ounce soft drinks and 5 pounds of ice in each. However, the drinks put into cooler A were refrigerated for several hours before they were packed in the cooler, while the drinks put into cooler B were at room temperature. When the picnickers open the two coolers three hours later, most of the ice in cooler A is still present, while nearly all of the ice in cooler B has melted. Explain this difference.

A 25.5-g aluminum block is warmed to 65.4 C and plunged into an insulated beaker containing 55.2 g water initially at 22.2 C. The aluminum and the water are allowed to come to thermal equilibrium. Assuming that no heat is lost, what is the final temperature of the water and aluminum?

If the internal energy of the products of a reaction is higher than the internal energy of the reactants, what is the sign of E for the reaction? In which direction does energy flow?

Explain the difference between an exothermic and an endothermic reaction. Give the sign of H for each type of reaction.

Instant cold packs used to ice athletic injuries on the field contain ammonium nitrate and water separated by a thin plastic divider. When the divider is broken, the ammonium nitrate dissolves according to the endothermic reaction: In order to measure the enthalpy change for this reaction, 1.25 g of NH4NO3 is dissolved in enough water to make 25.0 mL of solution. The initial temperature is 25.8 C, and the final temperature (after the solid dissolves) is 21.9 C. Calculate the change in enthalpy for the reaction in kJ. (Use 1.0 g/mL as the density of the solution and 4.18 J/g # C as the specific heat capacity.)

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