Question

Unlike chemical reactions, for which mass is conserved, nuclear reactions result in slight changes in mass. When mass is lost, it becomes energy according to the equation

ΔE=Δm⋅c2

where ΔE is the energy in joules, Δm is the mass defect in kilograms, and c is the speed of light (c=3.00×108 m/s). The mass defect is the difference between the total mass of the products and the total mass of reactants. The following values can be used to calculate the mass defect.

Particle	Mass (g/mol)
01e	0.00054858
11H	1.00782
42He	4.00260

Part A

The sun produces energy via fusion. One of the fusion reactions that occurs in the sun is

411H→42He+201e

How much energy in joules is released by the fusion of 2.09 g of hydrogen-1?

Express your answer to three significant figures and include the appropriate units.

Answer 1

The balanced chemical equation is given.

4 ¹H₁ --------> ⁴He₂ + 2 ⁰e₁

We start with 2.09 g hydrogen; mole(s) of ¹H₁ taken = (2.09 g)/(1.00782 g/mol) = 2.07378 mole.

As per the stoichiometric equation,

4 mole ¹H₁ = 1 mole ⁴He₂ = 2 moles ⁰e₁.

Therefore, 2.07378 mole ¹H₁ = (2.07378 mole ¹H₁)*(1 mole ⁴He₂/4 mole ¹H₁) = 0.518447 mole ⁴He₂.

Again, 2.07378 mole ¹H₁ = (2.07378 mole ¹H₁)*(2 mole ⁰e₁/4 mole ¹H₁) = 1.03689 mole ⁰e₁.

The total mass of the reactants = (2.07378 mole)*(1.00782 g/mol) = 2.089997 g; the combined mass of the products = [(0.518447 mole)*(4.00260 g/mol) + (1.03689 mole)*(0.00054858 g/mol)] = 2.075705 g.

Mass defect, Δm = (mass of products) – (mass of reactants) = (2.075705 g) – (2.089997 g) = -0.014292 g = -(0.014292 g)*(1 kg/1000 g) = -1.4292*10^-5 kg.

The energy involved, ΔE = Δm*c² = (-1.4292*10^-5 kg)*(3.00*10⁸ m/s)² = -1.28628*10¹² kg.m²s^-2 = -1.28628*10¹² J (1 J = 1 kg.m²s^-2) ≈ -1.29*10¹² J.

Since energy is released, ignore the negative sign and the energy released is 1.29*10¹² J (ans).