The sugar arabinose, C5H10O5, Molar Mass = 150.15 g/mole, was completely combusted with excess oxygen in a calorimeter. Combustion of a 0.548 g sample of arabinose caused the temperature to increase from 20.00 degrees C to 20.54 degrees C in a calorimeter with a total heat capacity of 15.8 kJ/degrees C. Calculate the enthalpy of combustion for arabinose.
Since no mass of water is given I assume the "total heat capacity of 15.8 kJ/degrees C" includes calorimeter + waters.
q = 15.8 kJ/C x delta T is heat in kJ.
If you want that per gram, divide q by 0.548 then per mole by multiplying that by molar mass arabinose.
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To calculate the enthalpy of combustion for arabinose, we need to use the formula:
Enthalpy of combustion = (q + qs) / moles of arabinose
Where:
q = heat transferred to the calorimeter during the reaction,
qs = heat absorbed by the surrounding water,
moles of arabinose = mass of arabinose / molar mass of arabinose.
First, let's calculate q, the heat transferred to the calorimeter.
q = C * ∆T
Where:
C = total heat capacity of the calorimeter (15.8 kJ/degrees C),
∆T = change in temperature (20.54 degrees C - 20.00 degrees C).
q = (15.8 kJ/degrees C) * (20.54 degrees C - 20.00 degrees C)
q = (15.8 kJ/degrees C) * 0.54 degrees C
q = 8.5 kJ
Next, let's calculate qs, the heat absorbed by the surrounding water.
qs = mass of water * specific heat capacity of water * ∆T
The specific heat capacity of water is 4.184 J/g·degrees C.
Since we have the total heat capacity of the calorimeter, we need to subtract the heat capacity due to the calorimeter itself.
mass of water = total heat capacity of calorimeter / specific heat capacity of water
mass of water = (15.8 kJ/degrees C) / (4.184 J/g·degrees C)
mass of water = 3775 g
qs = (3775 g) * (4.184 J/g·degrees C) * (20.54 degrees C - 20.00 degrees C)
qs = 334.1 J
Now, let's calculate the moles of arabinose.
moles of arabinose = mass of arabinose / molar mass of arabinose
moles of arabinose = 0.548 g / 150.15 g/mol
moles of arabinose = 0.00365 mol
Finally, let's calculate the enthalpy of combustion.
Enthalpy of combustion = (q + qs) / moles of arabinose
Enthalpy of combustion = (8.5 kJ + 334.1 J) / 0.00365 mol
Enthalpy of combustion = 2.33 MJ/mol
Therefore, the enthalpy of combustion for arabinose is 2.33 MJ/mol.
To calculate the enthalpy of combustion for arabinose, we need to determine the amount of heat released during the combustion process.
First, we need to find the heat absorbed by the calorimeter, which can be calculated using the equation:
q_calorimeter = (mass_calorimeter + mass_water) * specific_heat * ΔT
Here,
mass_calorimeter = mass of the calorimeter
mass_water = mass of the water
specific_heat = specific heat capacity of the water
ΔT = change in temperature
Given that the total heat capacity of the calorimeter is 15.8 kJ/°C, we can convert it to Joules by multiplying by 1000:
C_calorimeter = 15.8 kJ/°C * 1000 J/kJ = 15800 J/°C
Next, we calculate the heat absorbed by the calorimeter:
q_calorimeter = (15800 J/°C) * (20.54 - 20.00) °C = 856 J
Since the combustion reaction occurred under constant volume conditions, the heat absorbed by the calorimeter is equal to the heat released by the combustion reaction. Therefore, we can say that the heat released during combustion is 856 J.
Now, let's calculate the amount of arabinose combusted in moles:
moles_arabinose = mass_arabinose / molar_mass_arabinose
Given that the mass of arabinose combusted is 0.548 g and the molar mass of arabinose is 150.15 g/mol, we can substitute these values into the equation:
moles_arabinose = 0.548 g / 150.15 g/mol = 0.003652 mol
To determine the enthalpy change during the combustion of arabinose, we use the equation:
ΔH_combustion = q_combustion / moles_arabinose
Given that q_combustion (heat released during combustion) is 856 J and moles_arabinose is 0.003652 mol, we can calculate the enthalpy of combustion:
ΔH_combustion = 856 J / 0.003652 mol = 234,622 J/mol
Therefore, the enthalpy of combustion for arabinose is 234,622 J/mol.