Analytical solutions to reactive-transport equations describing the evolution of Li concentrations and isotopic ratios are presented for one-dimensional flow paths where reaction stoichiometry is constant along the flow path. These solutions are considered appropriate for chemical weathering in rapidly eroding catchments. The solutions may be described by two dimensionless numbers; 1) a Damkӧhler number describing the product of reaction rate and fluid residence time, and 2) a net partition coefficient which describes the fraction of Li re-precipitated in secondary minerals as the product of a fluid-secondary mineral partition coefficient and the mass fraction of secondary mineral precipitates. In settings where water entering flow paths is dilute, Li concentrations will increase along the flow path until they reach a limiting value determined by the net partition coefficient. Simultaneously, 7Li/6Li isotopic ratios will increase to a limiting value of the source rock ratio minus the secondary mineral-fluid Li-isotopic fractionation factor. Waters with Li-isotopic ratios in excess of this limiting value must have evolved with a change of reaction stoichiometry and/or partition coefficient along the flow path such that at some point net removal of Li to secondary minerals exceeds that supplied by dissolution of primary minerals. The modelling shows that the multiple controls on chemical weathering rates (temperature, rainfall, erosion rate, hydrology) cannot be inferred from Li concentration and isotopic ratio data alone which only provide two independent constraints. Caution should be exercised in interpretation of oceanic Li records in terms of potential climatic variables. The model is illustrated by a set of Li concentration and isotopic ratio measurements on river waters and bed sands in the Alaknanda river basin which forms the headwaters of the Ganges. This illustrates how values of the Damkӧhler number and net partition coefficient can be used to trace weathering processes. Water samples from catchments with similar lithologies and climates scatter along contours of approximately constant net partition coefficient, reflecting similar reaction stoichiometries, but with more variable Damkӧhler numbers reflecting variations in flow path length, fluid flux and/or reaction rate. Samples from the lower, warmer and less rapidly eroding catchments have high 7Li/6Li isotopic ratios with lower Li concentrations and must reflect at least a two-stage weathering process where reaction stoichiometry and/or Li fluid-mineral partition coefficients change along the flow path so that net Li is removed in the later stages.