We present a quantitative model for predicting the level of difficulty subjects will experience with specific problems. The model explicitly accounts for the number of subproblems a problem can be broken into and the difficultly of each subproblem. Although the model builds on previously published models, it is uniquely suited for blending with qualitative methods for the study of problem-solving "processes" rather than being limited to examination of final answers only. We illustrate the usefulness of the model by analysing the written solutions and think-aloud protocols of 17 subjects engaged with 25 chemical stoichiometry problems. We find that familiar themes for subject difficulty are revealed, including mapping of surface features, lack of interconnected knowledge hierarchy, and algorithmic operations at the expense of conceptual understanding. (Contains 2 tables and 6 figures.)