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As per Einstein relationship, $E=mc^2$ or its more correct form $E=\sqrt{(mc^2)^2 + (pc)^2}$. The mass loss would be extremely tiny given how little energy is exchanged in chemical reactions. But is there definite evidence to show that the energy contained in chemical bonds does not increase mass?

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  • $\begingroup$ Do not mix different concepts, e- is stable, normally there is no mass loss. In heavy atoms, a similar expression holds to take into account relativistic effects : the mass increases and the wave function is contracted. Another example, the effective mass in solid-state as an emergent phenomenon. $\endgroup$
    – M06-2x
    May 18, 2023 at 1:07
  • $\begingroup$ Chem+Math Expression formatting reference: MathJax Basics / Chem+Math expressions/formulas/equations / Upright vs italic / Math SE Mathjax tutorial // MathJax is preferred not to be used in CH SE Q titles. $\endgroup$
    – Poutnik
    May 18, 2023 at 4:29
  • $\begingroup$ At measurement of two compared quantities, there could be evidence their difference is statistically significant ( The mass has changed. ) or insignificant ( The mass does not change more than the limit the method can distinguish.) // By other words, there can be evidence they are not equal, there cannot be evidence they are equal. $\endgroup$
    – Poutnik
    May 18, 2023 at 7:22

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You are correct that the energy difference would be tiny, however you are incorrect that the mass would increase. The formation of bonds would release energy, therefore the mass would actually decrease instead of increase.

Let us consider hydrogen molecule with bonding energy of $436\ \mathrm{kJ/mol}$, which is approximately $7.24\times10^{-19}\ \mathrm J$ for one molecule. In term of mass, that would be
$$\Delta m=\frac E{c^2}=\frac{7.24\times10^{-19}\ \mathrm J}{8.99\times10^{16}\ \mathrm{m/s}}=8.05\times10^{-36}\ \mathrm{kg}$$ Mass of a hydrogen molecule ($\ce{H2}$) would be $3.34\times10^{-27}\ \mathrm{kg}$, which mean the mass lost is approximately $2.4\ \mathrm{ppb}$, which is pretty insignificant. And I believe is beyond the sensitivity of most of balance in chemistry lab.

So yes, there is a mass difference, and yes it is small, and – as far as I know – beyond the current capability of most our balance in chemistry lab to measure.

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  • $\begingroup$ youtu.be/Xo232kyTsO0 $\endgroup$
    – Tensor
    May 18, 2023 at 5:32
  • $\begingroup$ Depends on what they form from say Carbon and hydrogen to ethyne. $\endgroup$ May 18, 2023 at 6:45
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    $\begingroup$ It could be easier to calculate the relative mass change at molar, rather than molecular level. $\endgroup$
    – Poutnik
    May 18, 2023 at 6:49

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