  A cyclically operating chemical engine is considered that converts chemical
energy into mechanical work. The working fluid is a gas of finite-sized
spherical particles interacting through elastic hard collisions. For a generic
transport law for particle uptake and release, the efficiency at maximum power
$\eta$ takes the form 1/2+c\Delta \mu + O(\Delta \mu^2), with 1/2 a universal
constant and $\Delta \mu$ the chemical potential difference between the
particle reservoirs. The linear coefficient c is zero for engines featuring a
so-called left/right symmetry or particle fluxes that are antisymmetric in the
applied chemical potential difference. Remarkably, the leading constant in
$\eta$ is non-universal with respect to an exceptional modification of the
transport law. For a nonlinear transport model we obtain \eta = 1/(\theta +1),
with \theta >0 the power of $\Delta \mu$ in the transport equation
