The combustion of 0.1584 g benzoic acid increases the temperature of a bomb calorimeter by 2.54

The combustion of 0.1584 g benzoic acid increases the...

The combustion of $0.1584 \mathrm{~g}$ benzoic acid increases the temperature of a bomb calorimeter by $2.54^{\circ} \mathrm{C}$. Calculate the heat capacity of this calorimeter. (The energy released by combustion of benzoic acid is $26.42 \mathrm{~kJ} / \mathrm{g} .$ ) A $0.2130-\mathrm{g}$ sample of vanillin $\left(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\right)$ is then burned in the same calorimeter, and the temperature increases by $3.25^{\circ} \mathrm{C}$. What is the energy of combustion per gram of vanillin? Per mole of vanillin?

Key Concepts

Bomb Calorimetry

Bomb calorimetry is an experimental technique used to measure the energy change during chemical reactions, especially combustion. In a bomb calorimeter, the reaction occurs in a sealed, constant-volume container, and the heat released is absorbed by the surrounding water or another medium. This method allows for precise measurement of the energy content of a substance by monitoring the resultant temperature change.

Heat Capacity

Heat capacity is a property of a calorimeter that indicates the amount of energy required to raise its temperature by one degree Celsius. It is a crucial concept in calorimetry because, by knowing the heat capacity, the total energy released or absorbed during a reaction can be calculated from the observed temperature change. This conversion ensures that experimental temperature measurements can be directly related to energy changes in a system.

Combustion Energy Calculation

Combustion energy calculation involves determining the total energy released during a combustion reaction by multiplying the mass of the substance combusted by its known energy release per unit mass. This approach allows one to determine the overall heat output of the reaction, assuming that the value for energy per gram is provided or can be deduced from calibration data.

Energy per Gram and Energy per Mole

This concept involves converting the measured or calculated energy from the combustion process into energy per gram and further into energy per mole. Energy per gram is obtained by dividing the total energy by the mass of the sample, while energy per mole is calculated by multiplying the energy per gram by the molar mass of the substance, linking macroscopic measurements to molecular-scale energetic properties.

Calorimeter Calibration

Calorimeter calibration is the procedure used to determine the heat capacity of a calorimetric device by using a substance with a known heat of combustion. By burning a substance such as benzoic acid, where the energy release per unit mass is well-established, one can relate the observed temperature change to the energy released, thereby calibrating the calorimeter. This calibration then allows for accurate energy measurements from subsequent experiments using the same apparatus.

Transcript

00:01 So for this question, we're given that the combustion of a .158 binaxazate acid increases the temperature of a bomb calorimeter by 2 .5 degrees, 2 .54 degrees.

00:15 And it's given that energy released by combustion of 1 grams of benzogic acid is 26 .42 kilojoules.

00:22 So for every grams is 26 .42 joules.

00:29 So the energy released, will be, for every gram, gram is 26 .42.

00:35 So we use 0 .1584.

00:39 That's a given benazzoic acid times the 26 .42.

00:43 We'll get 4 .185 kilojoules.

00:50 And given that, so now we can calculate the energy released by the reaction, which is temperature increase times the energy required to change the temperature by 1 degrees, which is the specific heat and times the, the, so yeah, so the delta t times the heat capacity.

01:12 Heat capacity of the calorimeter is the energy released by the temperature divided by the delta t, so which is this divided by the delta t, which is 2 .54 degrees celsius.

01:26 We'll eventually get 1 .65 kilojoules per c, per celsius.

01:36 And with that we can calculate the energy released by the reaction, delta t times the heat capacity.

01:41 The delta t is 3 .25 times the 1 .65 and we'll get 5 .36 kilojoules of energy.

02:03 And that means 5 .36 joules of energy was released by the combustion of 0 .133 grams of vanilla and that is the energy release per grams of an ellen is...

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