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

Answer: The energy released for 1 mole of hydrogen formed is $3.597\times 10^{-13}J$

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

$\Delta m=(2m_C)-(m_{Na}+m_{H})$

$\Delta m=(2\times 12.0000)-(22.989767+1.007825)=2.408\times 10^{-3}amu=3.997\times 10^{-30}kg$

(Conversion factor: $1amu=1.66\times 10^{-27}kg$ )

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

$E=\Delta mc^2$

$E=(3.997\times 10^{-30}kg)\times (3\times 10^8m/s)^2$

$E=3.597\times 10^{-13}J$

Hence, the energy released for 1 mole of hydrogen formed is $3.597\times 10^{-13}J$