Is there any evidence to show that chemistry does not represent a mass to energy exchange?

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?

• 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. May 18, 2023 at 1:07
• 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. May 18, 2023 at 4:29
• 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. May 18, 2023 at 7:22

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.