Even Kelvin, who is commonly "credited" with this idea, did not think so, see Passon, Kelvin's clouds and Yanes, Lord Kelvin and the End of Physics, Which He Never Predicted.
Kelvin's 1900 lecture at the Royal Institution in London, made famous by the "two clouds" was published under the title Nineteenth Century Clouds over the Dynamical Theory of Heat and Light, and can be read here. It was restricted to those two topics specifically, and did not say that there were no more major problems left in physics, nor did it call the clouds "small", as often confabulated (e.g. by Bohm). Kelvin said nothing of the sort elsewhere either.
The lasting popularity of this fable mirrors that of its cousin, the "ultraviolet catastrophe", see Where did Rayleigh derive the ultraviolet catastrophe? (he didn't). By the way, Kelvin's cloud two is, also commonly, misidentified as the latter, but neither he nor anybody else spoke of it until 1908. It was instead specific heat at low temperatures. Passon explains the reasons:
"However, the claim that “there is nothing new to be discovered in physics” is
nowhere to be found in the 1900 lecture, or in any of Kelvin’s other writings, and
Zubairy suspiciously called this quotation just “attributed” to Lord Kelvin... All this shows, that one is dealing with a narrative that has been carefully crafted in order to emphasize the rift between “classical” and “modern” physics.
Against the backdrop of something considered essentially complete (with just two small blemishes), the conceptual changes of modern physics appear even more sensational and dramatic.
This somewhat rhetorical function is further strengthened by calling Lord Kelvin a “leading physicist of the time” (Bohm, Clegg)... However, by the time of the lecture
in 1900 (at the age of 75), his lasting contributions to thermodynamics and electromagnetism had been made decades ago. By that time, Kelvin was widely regarded in the community as the last prominent adherent of a mechanical
world view... When Kelvin published
the revised version of his Baltimore Lectures in 1904 (including the “cloud lecture” in Appendix B), the reaction seemed (to quote Knudson again) “polite indifference, and it is hard to point to a physicist whose work was influenced by
The closest thing to the "end of physics" was said not by Kelvin but by another holdover mechanist, Michelson, at the inauguration of the Ryerson Physics Laboratory at the University of Chicago in 1894:"The more important fundamental laws and facts of physical science have all been discovered..." He then repeated it in his book Light Waves and their Uses (1903). But even Michelson only talked about fundamental physics, to which technicalities of molecular chemistry did not belong. Still, he expected them to be forthcoming in "the day not far distant", and promoted ether as the emerging "theory of everything":
The day seems not far distant when the converging lines from many apparently remote regions of thought will meet... Then the nature of the atoms, and the forces called into play in their chemical union... the explanation of cohesion, elasticity, and gravitation — all these will be marshaled into a single compact and consistent body of scientific knowledge... one of the grandest generalizations of modern science ... that all the phenomena of the physical universe are only different manifestations of the various modes of motion of one all-pervading substance — the ether." [quoted from Kragh, Quantum Generations, ch. 4]
Michelson's optimism was not widely shared either.