Calculate the mass of propane, C3H8(g), that must be burned in air to evolve the same quantity of energy as produced by the fusion of 1.0 g of hydrogen in the following fusion reaction: 4H ---> He + 2e-
Assume that all the products of the combustion of C3H8 are in their gas phases.
To calculate the mass of propane required to release the same amount of energy as the given fusion reaction, we first need to determine the energy released by the fusion of 1.0 g of hydrogen.
Given fusion reaction: 4H ---> He + 2e-
To calculate the energy released in this reaction, we need to use the mass-energy equivalence formula:
E = mc^2
Where:
E = energy released
m = mass
c = speed of light
Given:
Mass of hydrogen, m = 1.0 g
Speed of light, c = 2.998 × 10^8 m/s
Plugging in the values:
E = (1.0 g) × (2.998 × 10^8 m/s)^2
Now, calculate the energy released in this fusion reaction.
E = 8.996 × 10^16 J
Now, we need to determine the mass of propane required to release the same amount of energy.
To do this, we need to use the heat of combustion of propane, which is the amount of energy released when one mole of propane is burned completely.
The chemical equation for the combustion of propane is:
C3H8 + 5O2 ---> 3CO2 + 4H2O
The balanced equation shows that for every 1 mole of propane (C3H8), 3 moles of carbon dioxide (CO2) are formed.
We need to find the heat of combustion of propane, which is the amount of energy released when 1 mole of propane is burned.
The heat of combustion of propane is approximately -2220 kJ/mol.
To calculate the mass of propane, we can use the equation:
Energy released = moles of propane × heat of combustion
Converting -2220 kJ/mol to J/mol, we get -2220 × 10^3 J/mol.
Now, we can solve for the number of moles of propane:
8.996 × 10^16 J = moles of propane × (-2220 × 10^3 J/mol)
moles of propane = (8.996 × 10^16 J) / (-2220 × 10^3 J/mol)
moles of propane ≈ -4.06 × 10^10 mol
Since moles cannot be negative, we can disregard the negative sign.
Now, we need to determine the molar mass of propane (C3H8):
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol
Molar mass of propane (C3H8) = (3 × 12.01 g/mol) + (8 × 1.01 g/mol)
Molar mass of propane (C3H8) ≈ 44.11 g/mol
Finally, we can calculate the mass of propane required:
Mass of propane = moles of propane × molar mass of propane
Mass of propane = (-4.06 × 10^10 mol) × (44.11 g/mol)
Mass of propane ≈ -1.79 × 10^12 g
Since mass cannot be negative, we can disregard the negative sign.
Therefore, approximately 1.79 × 10^12 grams of propane must be burned in air to evolve the same amount of energy as produced by the fusion of 1.0 g of hydrogen.