We developed and validated a new instrument, called "Measuring Concept progressions in Acid-Base chemistry" (MCAB) and used it to better understand the progression of undergraduate students' understandings about acid-base chemistry. Items were developed based on an existing learning progression for acid-base chemistry. We used the Rasch rating scale model for validation and to gain understanding of how students at different ability levels conceptualize the topic. We then used latent class analysis (LCA) to place students into concept classes. We found that three concept classes were sufficient to describe students' various response patterns and that these concept classes described a progression of understanding related to acid-base chemistry. All items fit well with the Rasch model. The final 33-item instrument measured students along a continuous scale with a reliability of 0.74 and categorized students with a precision of 0.89. All students possessed nonscientific understandings of pH and the pH scale. However, even the most novice students displayed basic scientific understandings about how acid-base indicators work and the Arrhenius model of acids and bases. We discuss the utility of Rasch and LCA procedures for analysis of learning progression-based assessments and suggest a simple algorithm that can be used to help chemistry instructors diagnose students' misconceptions.