In order to calibrate a bomb calorimeter , 3000 g of water is added to the calorimeter. next,
1.08 x 10-2mol of ethanol (C2H6O) is combusted in the presence of excess oxygen according to
the equation,
C2H6O (l) + 3 O2 (g) > 3 H2O (l) + 2 CO2 (g)
DE = - 1365 kJ/mol .
Assuming that the temperature of the water increases by 0.966 oC calculate the heat capacity of the
empty calorimeter (the calorimeter without water). (Remember that the specific heat of water is 4.18
J/g K)
How much heat is added to the calorimeter and water with the combustion of the ethanol. That's 0.0108 mol x 1365 kJ/mol = ? and convert to J.
Then J heat = (mass H2O x specific heat H2O x delta T) + Ccal*delta T
Solve for Ccal.
To calculate the heat capacity of the empty calorimeter, we need to use the equation:
Q = mcΔT
Where:
Q is the heat transferred to the water and calorimeter,
m is the mass of water in grams,
c is the specific heat capacity of water in J/g·K, and
ΔT is the change in temperature of the water and calorimeter.
In this case, we know the values for m (3000 g) and c (4.18 J/g·K). We also know the change in temperature, which is given as 0.966 ºC. However, we need to convert this change in temperature to Kelvin as the specific heat capacity is given in J/g·K.
To convert the change in temperature to Kelvin, we use the formula:
K = ºC + 273.15
Therefore, the change in temperature in Kelvin will be:
ΔT = 0.966 + 273.15 = 274.116 K
Now, we can substitute the values into the equation:
Q = (3000 g) * (4.18 J/g·K) * (274.116 K)
Calculating this expression will give us the amount of heat transferred to the water and calorimeter (Q).
Next, we need to calculate the heat released during the combustion of ethanol (C2H6O). The change in energy (DE) for the combustion reaction is given as -1365 kJ/mol.
Since we have the number of moles of ethanol (1.08 x 10^-2 mol), we can calculate the heat released (q) for this amount of ethanol using the formula:
q = DE * n
Where:
q is the heat released,
DE is the change in energy of the reaction (in kJ/mol), and
n is the number of moles of ethanol.
Substituting the values:
q = (-1365 kJ/mol) * (1.08 x 10^-2 mol)
Calculating this expression will give us the heat released (q).
Finally, since heat is conserved in a closed system, the heat released during the combustion of ethanol is equal to the heat absorbed by the water and calorimeter:
q = Q
Therefore, we can equate the expressions for q and Q:
(-1365 kJ/mol) * (1.08 x 10^-2 mol) = (3000 g) * (4.18 J/g·K) * (274.116 K)
Now, we can solve this equation for the heat capacity of the empty calorimeter.