A sample consisting of 0.025 mol of a solid compound is placed inside a metal cylinder. The cylinder was immersed in a water bath consisting of 10.00 kg of water at an original temperature of 25.00 °C. When the compound decomposes, the temperature of the water rises to 29.52 °C. Assume that the heat capacity of the cylinder is negligible. The specific heat of water is 4.184 J/(°C.g).
a. Calculate the heat evolved (in kJ) during the decomposition reaction, and from that determine the molar enthalpy change of the decomposition reaction.
I did this for you earlier.
To calculate the heat evolved during the decomposition reaction, we can use the formula:
q = m * c * ΔT
where:
q is the heat evolved (in J),
m is the mass of the water (in g),
c is the specific heat of water (in J/(°C.g)),
ΔT is the change in temperature of the water (in °C).
First, let's calculate the mass of the water in grams:
mass of water = 10.00 kg * 1000 g/kg = 10,000 g
Next, we need to calculate the change in temperature of the water:
ΔT = final temperature - initial temperature
ΔT = 29.52 °C - 25.00 °C = 4.52 °C
Now, we can calculate the heat evolved:
q = 10,000 g * 4.184 J/(°C.g) * 4.52 °C
q = 189,369.6 J
Since the question asks for the heat evolved in kJ, we can convert the result:
q = 189,369.6 J * (1 kJ / 1000 J)
q = 189.37 kJ
Now, to determine the molar enthalpy change of the decomposition reaction, we need to divide the heat evolved (in kJ) by the amount of substance in moles:
molar enthalpy change = heat evolved / amount of substance
The amount of substance is given as 0.025 mol. So,
molar enthalpy change = 189.37 kJ / 0.025 mol
molar enthalpy change = 7,574.8 kJ/mol (rounded to one decimal place)
Therefore, the heat evolved during the decomposition reaction is 189.37 kJ, and the molar enthalpy change of the reaction is 7,574.8 kJ/mol.