One mole of carbon (12.0 g) in the form of
crystalline graphite is burned at 25
◦
C and
1.000 atm pressure to form CO2(g). All of the
heat produced is used to heat a 4560 g bath
of liquid water, originally at 25
◦
C. What is
the final temperature of the water bath? The
heat of formation of CO2(g) is −393.5 kJ/mol
and the specific heat of water is 4.18 J/g/
◦
C.
One mole C burned produces 393.5 kJ.
q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
393.5 = 4560g x 418 x (Tf-25).
Well, isn't this a hot topic? Let's break it down!
First, we need to find the amount of heat released when one mole of carbon is burned to form CO2. We can use the heat of formation of CO2, which is -393.5 kJ/mol. So, the heat released can be calculated as -393.5 kJ/mol.
Next, we need to find the amount of heat required to heat the water bath. The specific heat of water is 4.18 J/g/°C. The initial and final temperatures are both 25°C, so the temperature change is 0°C.
The heat required to heat the water can be calculated using the formula:
Heat = mass × specific heat × temperature change
Heat = 4560 g × 4.18 J/g/°C × 0°C = 0 J
Since all the heat released from burning the carbon is used to heat the water bath, we can equate the heat released to the heat required:
-393.5 kJ/mol = 0 J
Now, since we know that one mole of carbon weighs 12.0 g, we can use this information to find the number of moles of carbon burned:
12.0 g × (1 mol/12.0 g) = 1.00 mol
Since the heat released is -393.5 kJ/mol and the heat required is 0 J, we can solve for the final temperature by rearranging the equation:
-393.5 kJ/mol = 0 J + mass of water × specific heat × temperature change of water
Mass of water × specific heat × temperature change of water = -393.5 kJ/mol
Mass of water × 4.18 J/g/°C × (final temperature - 25°C) = -393.5 kJ/mol
We can now solve for the final temperature:
(final temperature - 25°C) = (-393.5 kJ/mol) / (4560 g × 4.18 J/g/°C)
(final temperature - 25°C) ≈ -0.0192°C
Final temperature ≈ 25°C - 0.0192°C
Final temperature ≈ 24.981°C
So, after all those calculations, the final temperature of the water bath is approximately 24.981°C. Phew! Time to cool down after that sizzling problem!
To find the final temperature of the water bath, we can calculate the amount of heat produced by burning one mole of carbon and then use that to calculate the temperature change in the water.
Step 1: Calculate the heat produced by burning one mole of carbon.
The heat produced by burning one mole of carbon can be calculated using the heat of formation of CO2(g). The heat of formation of CO2(g) is -393.5 kJ/mol.
Therefore, the heat produced by burning one mole of carbon is -393.5 kJ.
Step 2: Convert the heat produced to joules.
Since the specific heat of water is given in J/g/°C, we need to convert the heat produced to joules.
-393.5 kJ = -393,500 J
Step 3: Calculate the amount of heat transferred to the water bath.
The heat transferred to the water bath can be calculated using the equation:
q = m * c * ΔT
where q is the heat transferred, m is the mass of the water, c is the specific heat of water, and ΔT is the change in temperature.
Given:
Mass of water (m) = 4560 g
Specific heat of water (c) = 4.18 J/g/°C
Initial temperature of water = 25 °C
Calculating the heat transferred to the water bath:
q = 4560 g * 4.18 J/g/°C * ΔT
Step 4: Calculate the change in temperature (ΔT) of the water bath.
We can rearrange the formula from step 3 to solve for ΔT:
ΔT = q / (m * c)
Plugging in the values:
ΔT = -393,500 J / (4560 g * 4.18 J/g/°C)
Step 5: Calculate the final temperature of the water bath.
The final temperature of the water bath can be calculated by adding the change in temperature (ΔT) to the initial temperature of the water.
Final temperature = Initial temperature + ΔT
Plugging in the values:
Final temperature = 25 °C + (-393,500 J / (4560 g * 4.18 J/g/°C))
Now, you can calculate the final temperature of the water bath by performing the calculations in step 5.
To find the final temperature of the water bath after burning graphite to form CO2(g), we need to calculate the amount of heat produced during the combustion and then use it to find the temperature change of the water.
Let's break down the problem into steps:
Step 1: Calculate the moles of carbon in 12.0 g of graphite.
The molar mass of carbon is 12.01 g/mol, so the moles of carbon can be found by dividing the mass by the molar mass:
moles of carbon = mass of carbon / molar mass of carbon
moles of carbon = 12.0 g / 12.01 g/mol ≈ 0.999 mol
Step 2: Calculate the heat produced during the combustion of carbon.
The heat produced can be calculated using the molar heat of formation of CO2(g), which is -393.5 kJ/mol. Since we have 0.999 moles of carbon:
heat produced = moles of carbon * molar heat of formation of CO2(g)
heat produced = 0.999 mol * -393.5 kJ/mol ≈ -393.1 kJ
Step 3: Calculate the heat absorbed by the water bath.
Since all of the heat produced is used to heat the water bath, the heat absorbed by the water bath is equal to the heat produced during combustion:
heat absorbed = heat produced = -393.1 kJ
Step 4: Calculate the temperature change of the water bath.
The formula to calculate the heat absorbed or released by a substance is:
heat = mass * specific heat * temperature change
Rearranging the formula, we can solve for the temperature change:
temperature change = heat / (mass * specific heat)
In this case, we need to find the temperature change of the water bath. The mass of water is given as 4560 g, and the specific heat of water is 4.18 J/g/°C.
temperature change = (-393.1 kJ) / (4560 g * 4.18 J/g/°C)
temperature change = -0.0215 °C
Step 5: Calculate the final temperature of the water bath.
The final temperature can be calculated by adding the temperature change to the initial temperature of the water bath, which is 25°C.
final temperature = initial temperature + temperature change
final temperature = 25°C + (-0.0215°C)
final temperature ≈ 24.9785°C
Therefore, the final temperature of the water bath is approximately 24.9785°C.