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.
Answer in units of
◦
C
gygyg
To find the final temperature of the water bath, we need to calculate the amount of heat released by burning one mole of carbon, and then use that heat to calculate the change in temperature of the water.
Step 1: Calculate the amount of heat released by burning one mole of carbon.
The heat released during the combustion of carbon can be calculated using Hess's Law. The heat of formation of CO2 is -393.5 kJ/mol. Since we are burning one mole of carbon, the amount of heat released will be the same.
Heat released by burning one mole of carbon = -393.5 kJ/mol
Step 2: Calculate the amount of heat transferred to the water bath.
The equation for heat transfer is given by:
q = m * C * ΔT
where q is the amount of heat transferred, m is the mass of the water, C is the specific heat capacity of water, and ΔT is the change in temperature.
Given:
Mass of water (m) = 4560 g
Specific heat capacity of water (C) = 4.18 J/g/°C
Step 3: Rearrange the equation to solve for ΔT:
ΔT = q / (m * C)
Step 4: Substitute the values into the equation and solve for ΔT:
ΔT = (-393.5 kJ/mol) / (4560 g * 4.18 J/g/°C)
Note: To make sure the units are consistent, it's important to convert kJ to J and grams to kilograms.
ΔT = (-393.5 * 10^3 J/mol) / (4560 * 10^-3 kg * 4.18 J/g/°C)
ΔT = -113.57 °C
Step 5: Calculate the final temperature of the water bath.
The final temperature can be calculated by adding the change in temperature to the initial temperature of the water bath.
Final temperature of the water bath = 25 °C - 113.57 °C
Final temperature of the water bath = -88.57 °C
Note: It's important to note that the final temperature is negative, indicating that the water bath has cooled down significantly due to the release of heat from the combustion reaction.