The enthalpy of combustion of benzoic acid (C_{6}H_{5}COOH) is c

fanyattehedzg

fanyattehedzg

Answered question

2022-01-11

The enthalpy of combustion of benzoic acid (C6H5COOH) is commonly used as the standard for calibrating constant-volume bomb calorimeters; its value has been accurately determined to be -3226.7 kJ/mol. When 1.9862 g of benzoic acid are burned in a calorimeter, the temperature rises from 21.84 to 25.67∘C. What is the heat capacity of the bomb? (Assume that the quantity of water surrounding the bomb is exactly 2000 g.)

Answer & Explanation

ambarakaq8

ambarakaq8

Beginner2022-01-12Added 31 answers

Step 1
Write a balanced thermochemical equation for the combustion of 1 mol of (C6H5COOH)
 C6H5COOH(aq)+12O2(g)⇒3H2O(l)+7CO2(g)ΔHrxn∘=−3226.7kJ/mol
Step 2
Calculate the molar mass of (C6H5COOH).
7(12.0107g/mol)+6(1.0079g/mol)+2(15.9994g/mol)=122.1211g/mo
Step 3
Calculate the heat of the reaction in joules:
1. Begin with the mass of the (C6H5COOH).
2. Use the molar mass of (C6H5COOH) as a conversion factor to convert grams of (C6H5COOH) to moles of (C6H5COOH).
3. Use a thermostoichiometric ratio to convert moles of (C6H5COOH) to kilojoules.
4. Use a conversion factor to convert kilojoules to joules.
qrxn=1.9862gC6H5COOlH1molC6H5COOH−3226.7kJ1000J122.1211gC6H5COOH1molC6H5COOH1kJ=−52480.J
Step 4
Since heat transfers from the reaction to the calorimeter and water, then (qw+qcal) must be equal in magnitude, but opposite in direction to qrxn. Expand both sides of the equation to include variables such as mass, temperature change, and specific heat capacity. Then solve for Ccal.
qrxn=−(qw+qcal)
qrxn=−qw−qcal
qrxn=−mw(ΔT)(sw)−Ccal(ΔT)
qrxn+mw(ΔT)(sw)=−Ccal(ΔT)
⇒

Don Sumner

Don Sumner

Skilled2023-05-29Added 184 answers

Step 1:
To solve the problem, we can use the formula for heat capacity:
C=qΔT
where C is the heat capacity of the bomb, q is the heat released by the combustion of benzoic acid, and ΔT is the change in temperature.
First, we need to calculate the heat released by the combustion of benzoic acid. The enthalpy of combustion of benzoic acid is given as -3226.7 kJ/mol. We can convert the mass of benzoic acid burned to moles using its molar mass.
The molar mass of benzoic acid (C6H5COOH) is calculated as follows:
C=12.01 g/mol
H=1.008 g/mol
O=16.00 g/mol
Molar mass of benzoic acid = (6×C)+(5×H)+O+O+H=122.12 g/mol
Step 2:
Now, we can calculate the number of moles of benzoic acid burned:
n=massmolar mass=1.9862g122.12g/mol
Next, we calculate the heat released:
q=n×ΔH
where ΔH is the enthalpy of combustion.
q=(1.9862g122.12g/mol)×−3226.7kJ/mol
Step 3:
Next, we need to calculate the change in temperature, ΔT, which is given as 25.67−21.84=3.83 degrees Celsius.
Finally, we can calculate the heat capacity of the bomb:
C=qΔT
C=−(1.9862g122.12g/mol)×3226.7kJ/mol3.83K
Simplifying the expression above gives the value of C in kJ/K.
nick1337

nick1337

Expert2023-05-29Added 777 answers

We know that the heat released by the combustion of benzoic acid is equal to the heat absorbed by the bomb and the water:
qbomb+qwater=0
The heat absorbed by the bomb can be calculated using the formula:
qbomb=Cbomb·ΔT
where ΔT is the change in temperature of the bomb.
The heat absorbed by the water can be calculated using the formula:
qwater=mwater·Cwater·ΔT
where m₋w is the mass of water and C₋w is the specific heat capacity of water.
Since the heat released by the combustion of benzoic acid is equal to the heat absorbed by the bomb and the water, we have:
Cbomb·ΔT+mwater·Cwater·ΔT=0
Substituting the given values:
Cbomb·(25.67−21.84)+2000·Cwater·(25.67−21.84)=0
Simplifying the equation:
Cbomb·3.83+2000·Cwater·3.83=0
Since we know the heat released by the combustion of benzoic acid is -3226.7 kJ/mol, we can calculate the number of moles of benzoic acid burned:
n=mbenzoic acidmolar mass of benzoic acid
Substituting the given values:
n=1.9862g122.12g/mol
Now we can calculate the heat capacity of the bomb:
Cbomb=heat releasedΔT=−3226.7kJ/moln·ΔT
Substituting the known values:
Cbomb=−3226.7kJ/moln·(25.67−21.84)
Finally, we can substitute the calculated value of Cᵦ into the first equation to solve for Cw:
Cbomb·3.83+2000·Cwater·3.83=0
Cwater=−Cbomb2000
RizerMix

RizerMix

Expert2023-05-29Added 656 answers

Solution:
q=m·C·ΔT
where:
- q is the heat transfer
- m is the mass
- C is the heat capacity
- ΔT is the change in temperature
First, we need to calculate the heat transfer (q). We can use the enthalpy of combustion of benzoic acid to determine the heat released during the combustion reaction.
Given that the enthalpy of combustion of benzoic acid is -3226.7 kJ/mol, we can calculate the number of moles of benzoic acid burned:
moles of benzoic acid=mass of benzoic acidmolar mass of benzoic acid
The molar mass of benzoic acid (C6H5COOH) can be calculated as:
molar mass of benzoic acid=6·molar mass of carbon+5·molar mass of hydrogen+molar mass of oxygen
The molar masses of carbon, hydrogen, and oxygen are:
molar mass of carbon=12.01g/mol
molar mass of hydrogen=1.008g/mol
molar mass of oxygen=16.00g/mol
Now, we can calculate the moles of benzoic acid burned:
moles of benzoic acid=1.9862gmolar mass of benzoic acid
Next, we can calculate the heat transfer (q) using the equation:
q=moles of benzoic acid·enthalpy of combustion of benzoic acid
q=moles of benzoic acid·(−3226.7kJ/mol)
To calculate the heat capacity (C) of the bomb calorimeter, we need to rearrange the equation:
C=qΔT·m
Given that the change in temperature (ΔT) is 25.67°C - 21.84°C and the mass (m) of the water surrounding the bomb is 2000 g, we can substitute the values into the equation:
C=qΔT·m
Finally, we can calculate the heat capacity (C) of the bomb calorimeter.

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