For the following fusion reaction, calculate the change in energy per mole.

2/1 H + 3/2 He -> 4/2 He + 1/1 H

See your post above.

To calculate the change in energy per mole for a fusion reaction, you can use Einstein's mass-energy equivalence principle, expressed by the famous equation E=mc². This equation relates the change in energy (ΔE) to the change in mass (Δm) during a nuclear reaction.

The first step is to calculate the change in mass (Δm) between the reactants and the products in the fusion reaction. In this case, we need to find the difference in mass between the reactants (2/1 H and 3/2 He) and the products (4/2 He and 1/1 H).

Looking at the atomic masses of hydrogen (H) and helium (He), we find that:

Mass of 2/1 H = 2.0141018 amu
Mass of 3/2 He = 3.0160308 amu
Mass of 4/2 He = 4.0026030 amu
Mass of 1/1 H = 1.0078250 amu

Now, subtract the sum of the masses of the reactants from the sum of the masses of the products:

2/1 H + 3/2 He = 2.0141018 amu + 3.0160308 amu = 5.0301326 amu
4/2 He + 1/1 H = 4.0026030 amu + 1.0078250 amu = 5.0104280 amu

Δm = (mass of products) - (mass of reactants)
= 5.0104280 amu - 5.0301326 amu
= -0.0197046 amu

Now that we have the change in mass (Δm), we can calculate the change in energy (ΔE) using the mass-energy equivalence principle:

ΔE = Δm * c²

Where c is the speed of light, approximately 2.998 × 10^8 m/s.

ΔE = (-0.0197046 amu) * (2.998 × 10^8 m/s)²
= (-0.0197046) * (2.998 × 10^8)² * (1.66053906660 × 10^-27 kg/amu) * (9 × 10^16 J/kg)
= -0.0197046 * 8.9880372803 * 10^-10 * 1.66053906660 * 10^-27 * 9 × 10^16 J
= -0.276 × 10^-10 J

Therefore, the change in energy per mole for this fusion reaction is approximately -0.276 × 10^-10 Joules per mole. Note that the negative sign indicates a decrease in energy or an exothermic reaction.