Suppose you burned 1.500 g of benzoic acid, C6 H5 CO2 H, in a constant-volume calorimeter and fo

Suppose you burned 1.500 g of benzoic acid, C6 H5 CO2 H, in...

Suppose you burned 1.500 g of benzoic acid, $\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H},$ in a constant-volume calorimeter and found that the temperature increased from $22.50^{\circ} \mathrm{C}$ to $31.69^{\circ} \mathrm{C}$. The calorimeter contained $\mathrm{d}$ dimeter cootainine calloin $1.669 \mathrm{dd}$ $775 \mathrm{g}$ of water, and the bomb had a heat capacity of $893 \mathrm{J} / \mathrm{K}$. Calculate $\Delta U$ per mole of benzoic acid. (FIGURE CANNOT COPY)

Key Concepts

Stoichiometry and Molar Conversions

Stoichiometry is the quantitative aspect of chemical reactions that relates the mass of reactants to the amount of substance in moles. It is applied in energy calculations by converting the energy change observed from a specific sample mass to a per-mole basis. This allows for standardized comparisons of the energetic properties of different substances, providing a deeper understanding of their combustion characteristics.

Energy Exchange in Combustion Reactions

In combustion reactions, the chemical energy stored in reactants is released as heat during the reaction. This released energy is transferred to the surroundings, such as a calorimeter, causing a measurable temperature increase. By precisely measuring this temperature change and accounting for the heat capacities of all components involved, the energy exchange can be quantified, reflecting the reaction’s internal energy change (?U).

Bomb Calorimeter

A bomb calorimeter is a specialized piece of equipment designed for constant-volume calorimetry, typically used to measure the heat of combustion of a substance. It consists of a strong sealed 'bomb' that withstands high pressures, surrounded by a water jacket. The heat released by the combustion reaction is absorbed by both the water and the calorimeter’s body, allowing for the determination of the internal energy change of the reaction.

Heat Capacity

Heat capacity is the amount of heat required to raise the temperature of a substance or system by one degree. In the context of calorimetry, knowing the heat capacity of both the calorimeter (including any surrounding water or other materials) is essential to calculate the total energy absorbed when a temperature change is observed. The combined heat capacity directly links the temperature change to the energy exchanged in the reaction.

Constant-Volume Calorimetry

Constant-volume calorimetry is an analytical technique where a reaction is performed in a sealed container so that the volume remains fixed. Under these conditions, the heat measured is directly related to the change in internal energy (?U) of the system, as no work is done due to volume expansion. This method is particularly useful for combustion reactions, where the energy produced is entirely absorbed by the calorimeter and its contents.

Transcript

00:01 Okay, i've written down everything we were given here we're given our initial and final temperature benzoic acid and a constant volume calorimeter the calorimeter contains 775 grams of water 1 .500 grams of benzoic acid initial and final temperature 893 joules per mole or joules per k blah blah blah, okay, so we know that q reaction plus q of our bomb plus the q of the water will equal zero heat transferred equals internal energy at constant volume okay, let's write our chemical equation so be let's do a three here a seven here 15 over 2 to keep that at 1 okay, q of our water will equal four point one eight four times seven seventy five grams, i should put my units in here j over g degrees c times i should have done my math here seven seventy five grams times thirty one point 69 degrees c minus twenty two point five zero degrees c so for q for water, i am getting two to nine seven ninety nine point five joules around later let's do q of the bomb and that will equal 893 j over k times thirty one point sixty nine minus twenty two point five zero do those are both degrees c and that will be 82? so now we're gonna q of the r will equal 8206 .7 plus twenty nine seven ninety nine point five joules and this will be negative.

03:14 So this will equal negative twenty -five three three seven no, i added that wrong there.

03:26 It did it again my little earbuds make noise thirty eight zero zero six joules there we go.

03:36 That's q r now, let's do our delta u in units of kilojoules per mole that'll equal negative thirty eight zero zero six joules divided by one point five zero zero grams times the molar mass of benzoic acid is 112 point one two i'm just gonna go verify this on my molar mass calculator wonder if they have benzoic acid in here.

04:21 We do blester -hart's one twelve point one two and this will equal okay, negative three eight zero zero six divided by parentheses one point five divided by one one two point one two close enter i'm getting a giant number here one point five let me check my numbers negative thirty eight zero sixty six is thirty eight divided by i'm getting negative twenty eight forty.

05:45 How much was my mass? one point five zero grams.

06:02 I'm gonna check my math here why am i getting twenty eight forty? i have negative thirty eight.

06:36 Oh six.

06:46 Let's try this another way negative thirty eight...

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