Nelson brings up vitalism in chapter 4, and suggests that Einstein's theory of Brownian motion was a deciding blow against the idea that biological material had a "vital force".
This was only one blow of many. Previously, I had heard that another severe blow to the idea was dealt by the Wöller's total sythesis of the urea molecule. Obviously, urea is a biological material (it is a main form of nitrogenous waste in humans). When Wöller showed you could synthesize it from non-living starting materials, this argued against "vital force".
However, it can also be argued that the impact of Wöller's work is overestimated: There are articles in J. of Chem. Educ.: