substance X has a molar mass of 107.6 g/mol. When 2.50 g of substance x burns in an iron calorimeter, the temp. of the calorimeter and the water (2.000 Kg) increases from 25.8 deg. C to 38.7 deg. C. What is the molar heat of combustion of substance X in KJ/Mole. Heat capacity of calorimeter is 0.555 kJ/deg C.
To find the molar heat of combustion of substance X, we need to calculate the heat released by the combustion reaction. We can then divide this value by the number of moles of substance X that burned to obtain the molar heat of combustion.
First, let's calculate the heat released by the combustion reaction. We can use the formula:
q = mcΔT
Where:
q = heat released (in Joules)
m = mass of water (in kg)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (final temperature - initial temperature)
Given:
Mass of water (m) = 2.000 kg
Specific heat capacity of water (c) = 4.18 J/g°C
Change in temperature (ΔT) = 38.7°C - 25.8°C = 12.9°C
Calculating the heat released:
q = (2.000 kg) * (4.18 J/g°C) * (12.9°C)
q = 107.268 J
To convert from Joules to kilojoules:
q = 107.268 J = 0.107268 kJ
Now, we need to calculate the number of moles of substance X that burned. To do this, we can use the molar mass of substance X.
Given:
Molar mass of substance X = 107.6 g/mol
Mass of substance X burned = 2.50 g
Calculating the number of moles:
moles of substance X = (mass of substance X burned) / (molar mass of substance X)
moles of substance X = (2.50 g) / (107.6 g/mol)
moles of substance X ≈ 0.0232 mol
Now, we can calculate the molar heat of combustion by dividing the heat released by the number of moles of substance X burned:
Molar heat of combustion = (q) / (moles of substance X)
Molar heat of combustion = (0.107268 kJ) / (0.0232 mol)
Molar heat of combustion ≈ 4.62 kJ/mol
Therefore, the molar heat of combustion of substance X is approximately 4.62 kJ/mol.