Question

When a lithium nucleus reacts with a proton according to the reaction 7Li + 1H -> 2 4He, 3.1 x 10^-29 kg of mass converted to energy. Calculate the energy released per mole of Li.

Answer 1

Mass lost during conversion of 7 nuclei of Li = 3.1 x 10^-29 kg.

Now, using, E = mc²

            Where, E = energy (in J) , m = mass converted into energy (in kg) , c = speed of light (in m/s)

Or,

Energy released from conversion of 7 Li nuclei = (3.1 x 10^-29 kg) x (3.0 x 10⁸ m/s)²

            Or, E = 2.79 x 10^-12 kg m² s^-2

            Or, E = 2.79 x 10^-12 J                                                                   [Note: 1 J = 1 kg m² s^-2]

Number of Li nuclei in 1 mol sample = 6.022 x 10²³

Since, 7 Li nuclei yield 2.79 x 10^-12 J energy

            Or, 1 -   -           (2.79 x 10^-12 / 7) J

            Or, 1 mol           (2.79 x 10^-12 / 7) x 6.022 x 10²³ J

                                    = 2.40 x 10¹¹ J

                                    = 2.40 x 10⁸ kJ = 2.40 x 10⁵ MJ

Hence, conversion of 1 mol Li nuclei produces 2.40 x 10⁸ kJ energy.