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 0.855 g of dimethylphthalate is combusted in a calorimeter whose heat capacity (Ccalorimeter) is 6.25 kJ/°C at 21.5 °C. What is the final temperature of the calorimeter?
To solve this problem, we will use the equation q = mcΔT, where q is the heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
First, we need to calculate the heat transferred during the combustion of dimethylphthalate. We can use the equation q = ΔHcomb * n, where ΔHcomb is the enthalpy of combustion and n is the number of moles of dimethylphthalate.
To find the number of moles, we can use the equation n = m/M, where m is the mass of dimethylphthalate and M is its molar mass.
Given that the mass of dimethylphthalate is 0.855 g and its molar mass is 194.18 g/mol, we can calculate n:
n = 0.855 g / 194.18 g/mol = 0.004405 mol
Next, we can calculate the heat transferred:
q = ΔHcomb * n
q = -4685 kJ/mol * 0.004405 mol = -20.6 kJ
Now, we can calculate the change in temperature of the calorimeter. We can rearrange the equation q = mcΔT to solve for ΔT:
ΔT = q / (mc)
Given that the heat capacity of the calorimeter is 6.25 kJ/°C and the initial temperature is 21.5 °C, we can calculate the change in temperature:
ΔT = -20.6 kJ / (6.25 kJ/°C)
ΔT = -3.296 °C
The change in temperature is negative because heat is transferred out of the calorimeter.
Finally, we can calculate the final temperature by subtracting the change in temperature from the initial temperature:
Final temperature = 21.5 °C - 3.296 °C = 18.204 °C
Therefore, the final temperature of the calorimeter is approximately 18.204 °C.