If 0.250 g of fuel increases the temperature of a calorimeter by 20 °C,
and the calorimeter is calibrated at 6.28 kJ/°C, calculate the heat of
combustion of fuel per mole of fuel. Please show full solutions!
just looking at the units, I'd say
20°C * 6.28kJ/°C = 125.8 kJ / 0.250g = 503.2 kJ/g
No idea how many moles that is for your fuel ...
To calculate the heat of combustion per mole of fuel, we need to first determine the amount of heat transferred to the calorimeter.
We can use the formula:
q = m * C * ΔT
where:
- q is the amount of heat transferred (in joules)
- m is the mass of the fuel (in grams)
- C is the specific heat capacity of the calorimeter (in joules per gram per degree Celsius)
- ΔT is the change in temperature (in degrees Celsius)
In this case, the mass of the fuel (m) is given as 0.250 grams, the change in temperature (ΔT) is 20 °C, and the specific heat capacity of the calorimeter (C) is given as 6.28 kJ/°C.
First, let's convert the units of the specific heat capacity from kJ/°C to J/g°C:
6.28 kJ/°C = 6.28 * 1000 J/°C = 6280 J/°C
Now, let's substitute the given values into the formula to calculate q:
q = (0.250 g) * (6280 J/°C) * (20 °C)
q = 31400 J
Next, we need to convert the amount of heat transferred (q) to moles of fuel. To do this, we need the molar mass of the fuel.
Assuming we know the formula of the fuel, we can determine the molar mass of the fuel by summing up the atomic masses of each element in the formula.
Once we have the molar mass, we can use the following conversion factor:
1 mole of fuel = molar mass of fuel (g)
Dividing the amount of heat transferred (q) by the mass of the fuel will give us the heat of combustion per mole of fuel:
Heat of combustion per mole of fuel = q / (mass of fuel in moles)
Let's assume the molar mass of the fuel is M grams/mole.
Heat of combustion per mole of fuel = 31400 J / (0.250 g / M)
Simplifying further:
Heat of combustion per mole of fuel = (31400 J * M) / 0.250 g
Now, substituting the actual molar mass of the fuel will give us the final answer.
Note: Since the molar mass of the fuel is not provided in the question, you will need to find it from additional information or perform a separate chemical analysis if necessary.
To calculate the heat of combustion of fuel per mole of fuel, we need to determine the amount of energy released by the combustion of 0.250 g of fuel, and then convert it to energy per mole.
First, let's convert the mass of fuel from grams to moles. To do this, we need to know the molar mass of the fuel, which can be found in the periodic table or given in the problem statement. Let's assume the molar mass of the fuel is M g/mol.
Using the molar mass, we can calculate the number of moles of fuel:
Number of moles = mass / molar mass = 0.250 g / M g/mol
Next, we need to calculate the energy released by the combustion of 0.250 g of fuel. This can be done using the equation:
Energy released = heat capacity of calorimeter * temperature change
Given:
- Heat capacity of calorimeter = 6.28 kJ/°C
- Temperature change = 20 °C
Energy released = 6.28 kJ/°C * 20 °C
Now, we have the energy released by the combustion of 0.250 g of fuel. To convert it to energy per mole, we need to divide by the number of moles of fuel.
Energy per mole of fuel = Energy released / Number of moles
Substituting the values:
Energy per mole of fuel = (6.28 kJ/°C * 20 °C) / (0.250 g / M g/mol)
Simplifying the equation:
Energy per mole of fuel = (6.28 kJ/°C * 20 °C) * (M g/mol / 0.250 g)
Now, we can calculate the energy per mole of fuel using the given values.