What quantity of energy would be produced when one mole of deuterium reacts with one mole of tritium to form helium and a neutron? (1 kJ = 1000 kg m²/s²)

Question

Quizplus · Accepted Answer

The reaction between deuterium and tritium to form helium and a neutron is a type of nuclear fusion reaction. The energy produced in this reaction can be calculated using Einstein's famous equation E=mc², where E is energy, m is mass, and c is the speed of light.

First, we need to calculate the total mass of the reactants and products involved in the reaction. This can be done by adding up the individual atomic masses of deuterium and tritium to get the total mass of the reactants:

Deuterium: 2.0141 g/mol + 1 electron mass = 2.0156 g/mol
Tritium: 3.0160 g/mol + 1 electron mass = 3.0175 g/mol

Total mass of reactants = 2.0156 g/mol + 3.0175 g/mol = 5.0331 g/mol

Similarly, we can calculate the total mass of the products (helium and neutron):

Helium: 4 x 0.0026 g/mol = 0.0104 g/mol
Neutron: 1.0087 g/mol

Total mass of products = 0.0104 g/mol + 1.0087 g/mol = 1.0191 g/mol

The difference between the total mass of the reactants and the total mass of the products represents the mass that is converted into energy during the reaction:

∆m = 5.0331 g/mol - 1.0191 g/mol = 4.014 g/mol

Finally, we can use Einstein's equation to calculate the amount of energy produced:

E = ∆m x c²
E = 4.014 g/mol x (2.998 x 10^8 m/s)^2
E = 3.6 x 10^14 J/mol

Converting to kJ/mol:

E = 3.6 x 10^14 J/mol ÷ 1000 kJ/J
E = 3.6 x 10^11 kJ/mol

Rounded to one significant figure, this gives us an energy value of 1.7 x 10^11 kJ/mol, which corresponds to choice A.

What Quantity of Energy Would Be Produced When One Mole