Question

It is believed that two carbon-12 nuclei can react in the core of a supergiant star to form sodium-23 and hydrogen-1. Calculate the energy released from this reaction for each mole of hydrogen formed. The masses of carbon-12, sodium-23, and hydrogen-1 are 12.0000 amu, 22.989767 amu, and 1.007825, respectively.

Answer 1

The energy released from the fusion of two carbon-12 nuclei to form sodium-23 and hydrogen-1 was calculated to be approximately 1.350 × 10⁷ MeV/mole of hydrogen-1 formed.

Step-by-step explanation:

To calculate the energy released from the fusion reaction where two carbon-12 nuclei react to form sodium-23 and hydrogen-1, we first determine the mass defect by subtracting the total final mass from the initial mass of the reactants:

• Initial mass: 2 × 12.0000 amu (carbon-12)
• Final mass: 22.989767 amu (sodium-23) + 1.007825 amu (hydrogen-1)

The mass defect (Δm) is found as: Δm = (2 × 12.0000 – 22.989767 – 1.007825) amu = 0.002408 amu.

Using Einstein's equation, E = Δmc², and considering 1 amu = 931.5 MeV/c²:

E = 0.002408 amu × 931.5 MeV/c²/amu = 2.243 MeV (per reaction).

To find the energy released per mole, we multiply the per-reaction energy by Avogadro's number (6.022 × 10²³ moles⁻¹):

E (per mole) = 2.243 MeV × 6.022 × 10²³ = 1.350 × 10⁷ MeV/mole

Thus, the energy released for each mole of hydrogen formed in this reaction is approximately 1.350 × 10⁷ MeV/mole.

Answer 2

Answer: The energy released for 1 mole of hydrogen formed is
`3.597* 10^(-13)J`

Step-by-step explanation:

First we have to calculate the mass defect
`(\Delta m)`.

The equation for the fusion of two carbon-12 nuclei follows:

`_(6)^(12)\textrm{C}+_(6)^(12)\textrm{C}\rightarrow _(11)^(23)\textrm{Na}+_1^(1)\textrm{H}`

To calculate the mass defect, we use the equation:

Mass defect = Sum of mass of reactant - Sum of mass of product

`\Delta m=(2m_C)-(m_(Na)+m_(H))`

`\Delta m=(2* 12.0000)-(22.989767+1.007825)=2.408* 10^(-3)amu=3.997* 10^(-30)kg`

(Conversion factor:
`1amu=1.66* 10^(-27)kg` )

To calculate the energy released, we use Einstein equation, which is:

`E=\Delta mc^2`

`E=(3.997* 10^(-30)kg)* (3* 10^8m/s)^2`

`E=3.597* 10^(-13)J`

Hence, the energy released for 1 mole of hydrogen formed is
`3.597* 10^(-13)J`