A bomb calorimetric experiment was run to determine the...

A bomb calorimetric experiment was run to determine the enthalpy of combustion of ethanol. The reaction is $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) $$ The bomb had a heat capacity of $550 \mathrm{J} / \mathrm{K},$ and the calorimeter contained $650 \mathrm{g}$ of water. Burning $4.20 \mathrm{g}$ of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)$ resulted in a rise in temperature from $18.5^{\circ} \mathrm{C}$ to $22.3^{\circ} \mathrm{C}$. Calculate $\Delta U$ for the combustion of ethanol, in $\mathrm{kJ} / \mathrm{mol}$.

A bomb calorimetric experiment was run to determine the enthalpy of combustion of ethanol. The reaction is
$$
\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell)
$$
The bomb had a heat capacity of $550 \mathrm{J} / \mathrm{K},$ and the calorimeter contained $650 \mathrm{g}$ of water. Burning $4.20 \mathrm{g}$ of ethanol, $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)$ resulted in a rise in temperature from $18.5^{\circ} \mathrm{C}$ to $22.3^{\circ} \mathrm{C}$. Calculate $\Delta U$ for the combustion of ethanol, in $\mathrm{kJ} / \mathrm{mol}$.

Key Concepts

Bomb Calorimetry

Bomb calorimetry is an experimental technique used to measure the heat energy released or absorbed during a chemical reaction, typically combustion, in a controlled, constant volume environment. It involves a sealed container (the bomb) in which the reaction occurs, and the energy change is determined by measuring the temperature change of the surrounding water bath and the calorimeter's heat capacity.

Heat Capacity

Heat capacity is the amount of heat required to raise the temperature of a system by one degree. In calorimetric experiments, the overall heat capacity of the calorimeter (including both the bomb and any surrounding water) is used to calculate the total energy change from the observed temperature change, providing insight into the energy released or absorbed during the reaction.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates the amount of heat required to raise the temperature of one gram of the substance by one degree. In calorimetry, the specific heat capacity of water is used alongside its mass to calculate the heat absorbed by the water, which in turn helps determine the energy change of the reaction taking place in the calorimeter.

Stoichiometry

Stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It is used to convert the mass of a substance into moles, allowing the determination of energy change per mole of reactant when combined with calorimetric data, which is essential for comparing experimental values to standard thermodynamic quantities.

Internal Energy Change (?U)

Internal energy change (?U) represents the total energy change of a system at constant volume, excluding work done by expansion. In bomb calorimetry, the measurement directly reflects ?U, as the reaction is performed in a sealed, constant-volume container. This allows for the calculation of the energy change on a per-mole basis, providing important thermodynamic data about the reaction.

Transcript

00:01 Okay, so the first thing that we have to do is calculate the amount of energy released by 4 .2 grams of ethanol.

00:09 So we can do that by calculating the amount of energy needed to raise the temperature of the bomb calorimeter and water from 18 .5 degrees celsius to 22 .3 degrees celsius.

00:21 So the first thing that we can do is let's calculate delta t.

00:25 So delta t is equal to the temperature final minus the temperature initial.

00:31 So the temperature final is 22 .3 degrees celsius.

00:37 So let's convert that into kelvin's plus 273 minus 18 .5 degrees celsius plus 273.

00:44 That is also the conversion to kelvin, right? and we get duttsy to be equal to 3 .8 kelvin.

00:51 Now let's calculate how much energy is needed to raise the water from 18 .5 degrees celsius to 22 .3 degrees celsius.

00:59 So q is equal to m, so 650 grams.

01:04 C is 4 .182 joules per gram times kelvin.

01:08 That is the specific heat constant for water.

01:14 And delta t we calculated as 3 .8 kelvin.

01:17 Right.

01:18 Kelvin cancels, gram cancels, we're left for joules.

01:21 And we get q is equal to 103 to 9 .54.

01:28 Now let's calculate the amount of energy needed to raise the bottom colorimeter by 3 .8 degrees celsius.

01:35 So q is equal to c of bond which is 550 joules per kelvin and then we multiply that by the change in temperature which is 3 .8 kelvin right kelvin cancels or less of joules...

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