3.5 g of a hydrocarbon fuel is burned in a ves-
sel that contains 250. grams of water initially
at 25.00 C. After the combustion, the temper-
ature of the water is 26.55 C. How much heat
is evolved per gram of fuel burned?
heat evolved = q = mass H2O x specific heat H2O x (Tfinal-Tinitial)
heat/g = q/3.5
8,992.65714
To find the amount of heat evolved per gram of fuel burned, we can use the equation:
Q = mcΔT
Where
Q = heat evolved (in joules)
m = mass of water (in grams)
c = specific heat capacity of water (4.18 J/g·°C)
ΔT = change in temperature of water (in °C)
First, we need to find the change in temperature of the water:
ΔT = final temperature - initial temperature
ΔT = 26.55°C - 25.00°C
ΔT = 1.55°C
Next, we can calculate the amount of heat evolved:
Q = mcΔT
Q = (250 g)(4.18 J/g·°C)(1.55°C)
Q = 1619.5 J
To find the amount of heat evolved per gram of fuel burned, we divide the heat evolved by the mass of the fuel:
Heat evolved per gram of fuel burned = Q / mass of fuel
Heat evolved per gram of fuel burned = 1619.5 J / 3.5 g
Heat evolved per gram of fuel burned ≈ 462.71 J/g
Therefore, approximately 462.71 joules of heat are evolved per gram of fuel burned.
To determine the amount of heat evolved per gram of fuel burned, we need to calculate the heat exchanged during the combustion process.
First, let's calculate the heat exchanged between the fuel and the water using the formula:
Q = mcΔT
Where:
Q = heat exchanged (in Joules)
m = mass of water (in grams)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (final temperature - initial temperature) of the water (in °C)
Given:
mass of water (m) = 250. grams
initial temperature of water = 25.00 °C
final temperature of water = 26.55 °C
Substituting the values into the formula, we have:
Q = (250. g) × (4.18 J/g°C) × (26.55 °C - 25.00 °C)
Simplifying,
Q = (250. g) × (4.18 J/g°C) × (1.55 °C)
Q = 1619.75 J
Now, let's calculate the heat evolved per gram of fuel burned.
To do this, we need to convert the mass of the hydrocarbon fuel from grams to moles. We can then use the balanced combustion equation to determine the molar ratio between the fuel and the heat evolved.
Given:
mass of hydrocarbon fuel = 3.5 g
To convert the mass to moles, we need to know the molar mass of the hydrocarbon fuel. Let's assume it is CxHy, and the molar masses of carbon (C) and hydrogen (H) are 12.01 g/mol and 1.008 g/mol, respectively.
Let's calculate the moles of carbon and hydrogen in the fuel:
Moles of carbon (nC) = mass of carbon / molar mass of carbon
Moles of hydrogen (nH) = mass of hydrogen / molar mass of hydrogen
Since the molar ratio between carbon and hydrogen in the fuel is 1:ratio, we can assume that the ratio of carbon to hydrogen is the same as the molar ratio of carbon to hydrogen in the hydrocarbon fuel.
Next, let's calculate the moles of hydrocarbon fuel burned:
Moles of fuel = min(nC, nH)
Now, we can use the balanced combustion equation to determine the molar ratio between the fuel and the heat evolved:
CxHy + (x + (y/4))O2 → xCO2 + (y/2)H2O
The balanced equation indicates that for every x moles of fuel burned, x moles of CO2 and (y/2) moles of H2O are formed.
Based on the equation, the heat evolved per mole of fuel burned is the same as the heat exchanged between the water and the fuel (Q).
Finally, we can calculate the heat evolved per gram of fuel burned:
Heat evolved per gram of fuel burned = Q / (moles of fuel / mass of fuel)
Substituting the previously calculated values, we get:
Heat evolved per gram of fuel burned = 1619.75 J / (moles of fuel / 3.5 g)