Phthalates used as plasticizers in rubber and plastic products are believed to act as hormone mimics in humans. The value of ΔHcomb for dimethylphthalate (C10H10O4) is –4685 kJ/mol. Assume 0.900 g of dimethylphthalate is combusted in a calorimeter whose heat capacity (Ccalorimeter) is 6.65 kJ/°C at 20.5 °C. What is the final temperature of the calorimeter?
To determine the final temperature of the calorimeter, we need to use the heat transfer equation:
q = m*CΔT
Where:
q = heat transfer
m = mass of the substance
C = specific heat capacity
ΔT = change in temperature
First, let's calculate the heat released during the combustion of dimethylphthalate:
Step 1: Convert the mass of dimethylphthalate (0.900 g) to moles.
To do this, we need the molar mass of dimethylphthalate, which is:
(2 * 12.011 g/mol) + (10 * 1.008 g/mol) + (4 * 15.999 g/mol) = 194.18 g/mol
0.900 g * (1 mol / 194.18 g) ≈ 0.00463 mol
Step 2: Calculate the heat released during combustion.
The heat released during combustion (ΔHcomb) for dimethylphthalate is given as -4685 kJ/mol.
Heat released = ΔHcomb * moles of dimethylphthalate
Heat released = -4685 kJ/mol * 0.00463 mol = -21.67 kJ
Step 3: Calculate the change in temperature of the calorimeter.
We know that the heat capacity of the calorimeter (Ccalorimeter) is 6.65 kJ/°C and the change in temperature (ΔT) is the final temperature minus the initial temperature.
q = m*CΔT (rearranging the equation)
-21.67 kJ = 6.65 kJ/°C * ΔT
ΔT = (-21.67 kJ) / (6.65 kJ/°C)
ΔT = -3.26 °C
The negative sign indicates that the temperature of the calorimeter has decreased.
Step 4: Calculate the final temperature of the calorimeter.
To determine the final temperature, we need to subtract the change in temperature (ΔT) from the initial temperature of the calorimeter, which is 20.5 °C.
Final temperature = Initial temperature - ΔT
Final temperature = 20.5 °C - (-3.26 °C)
Final temperature ≈ 23.76 °C
Therefore, the final temperature of the calorimeter is approximately 23.76 °C.