2.1 g of a hydrocarbon fuel is burned in a calorimeter that contains 280 grams of water initially at 25.00◦C. After the combustion, the temperature is 26.55◦C. How much heat is evolved per gram of fuel burned? The heat capacity of the calorimeter (hardware only) is 92.3 J/◦C.
1. 14014 J/g
2. 143 J/g
3. 932 J/g
4. 14879 J/g
5. 29431 J/g
6. 1958 J/g
7. 1815 J/g
8. 864 J/g
q = [mass H2O x specific heat H2O x (Ttinal-Tinitial)] + Ccal x (Tfinal-Tinitial) and that gives you q for 2.1. Change to q for 1 g.
To find the heat evolved per gram of fuel burned, we need to first calculate the heat absorbed by the water and the calorimeter. We can use the equation:
q = mcΔT
where q is the heat absorbed, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat absorbed by the water:
m_water = 280 g
c_water = 4.18 J/g°C (specific heat capacity of water)
ΔT_water = 26.55°C - 25.00°C = 1.55°C
q_water = m_water * c_water * ΔT_water
= 280 g * 4.18 J/g°C * 1.55°C
= 1815.92 J
Next, we need to calculate the heat absorbed by the calorimeter:
c_calorimeter = 92.3 J/°C (heat capacity of the calorimeter)
ΔT_calorimeter = ΔT_water = 1.55°C
q_calorimeter = c_calorimeter * ΔT_calorimeter
= 92.3 J/°C * 1.55°C
= 143.165 J
Now, to find the total heat evolved, we sum up the heat absorbed by the water and the calorimeter:
q_total = q_water + q_calorimeter
= 1815.92 J + 143.165 J
= 1959.085 J
Finally, we divide the total heat evolved by the mass of the fuel burned:
m_fuel = 2.1 g
q_per_gram = q_total / m_fuel
= 1959.085 J / 2.1 g
≈ 933.85 J/g
Rounded to two decimal places, the heat evolved per gram of fuel burned is approximately 933.85 J/g. Therefore, the correct answer is option 3: 932 J/g.
To find the heat evolved per gram of fuel burned, we need to calculate the amount of heat transferred to the water in the calorimeter.
The formula we can use to calculate heat is:
Heat (q) = mass (m) × specific heat capacity (c) × change in temperature (ΔT)
First, we need to find the mass of water in the calorimeter. Given that the initial mass of water is 280 grams, we can use this value directly.
Next, we need to calculate the change in temperature (ΔT). The initial temperature is 25.00°C, and after combustion, the temperature becomes 26.55°C. The change in temperature is:
ΔT = final temperature - initial temperature
ΔT = 26.55°C - 25.00°C
ΔT = 1.55°C
Now, we can calculate the amount of heat transferred to the water.
Heat (q) = mass of water (m) × specific heat capacity of water (c) × ΔT
Specific heat capacity of water (c) is approximately 4.18 J/g°C.
Heat (q) = 280 g × 4.18 J/g°C × 1.55°C
Heat (q) = 1831.2 J
However, this value includes the heat capacity of the calorimeter hardware. To find the heat evolved per gram of fuel burned, we need to subtract the heat absorbed by the calorimeter.
The heat capacity of the calorimeter hardware is given as 92.3 J/°C. Since the change in temperature is 1.55°C, the heat absorbed by the calorimeter is:
Heat absorbed by calorimeter = heat capacity of calorimeter × ΔT
Heat absorbed by calorimeter = 92.3 J/°C × 1.55°C
Heat absorbed by calorimeter = 142.765 J
Finally, to find the heat evolved per gram of fuel burned, we divide the net heat transferred to the water (q) by the mass of the fuel burned (2.1 g).
Heat evolved per gram of fuel burned = (heat transferred to water - heat absorbed by calorimeter) / mass of fuel burned
Heat evolved per gram of fuel burned = (1831.2 J - 142.765 J) / 2.1 g
Heat evolved per gram of fuel burned = 1688.435 J / 2.1 g
Heat evolved per gram of fuel burned ≈ 803 J/g
Therefore, none of the provided options match the calculated value.