The analysis of a sample generates a chemical or physical signal that is proportional to the amount of analyte in the sample. This signal may be anything we can measure, such as volume or absorbance. It is convenient to divide analytical techniques into two general classes based on whether the signal is proportional to the mass or moles of analyte, or is proportional to the analyte’s concentration Consider the two graduated cylinders in Figure 3.3.1 , each of which contains a solution of 0.010 M Cu(NO 3 ) 2 . Cylinder 1 contains 10 mL, or \(1.0 \times 10^{-4}\) moles of Cu 2 + , and cylinder 2 contains 20 mL, or \(2.0 \times 10^{-4}\) moles of Cu 2 + . If a technique responds to the absolute amount of analyte in the sample, then the signal due to the analyte S A \[S_A = k_A n_A \label{3.1}\] where n A is the moles or grams of analyte in the sample, and k A is a proportionality constant. Because cylinder 2 contains twice as many moles of Cu 2 + as cylinder 1, analyzing the contents of cylinder 2 gives a signal twice as large as that for cylinder 1. A second class of analytical techniques are those that respond to the analyte’s concentration, C A \[S_A = k_A C_A \label{3.2}\] Since the solutions in both cylinders have the same concentration of Cu 2 + , their analysis yields identical signals. A technique that responds to the absolute amount of analyte is a total analysis technique. Mass and volume are the most common signals for a total analysis technique, and the corresponding techniques are gravimetry ( Chapter 8 ) and titrimetry ( Chapter 9 ). With a few exceptions, the signal for a total analysis technique is the result of one or more chemical reactions, the stoichiometry of which determines the value of k A in Equation \ref{3.1}. Historically, most early analytical methods used a total analysis technique. For this reason, total analysis techniques are often called “classical” techniques. Spectroscopy ( Chapter 10 ) and electrochemistry ( Chapter 11 ), in which an optical or an electrical signal is proportional to the relative amount of analyte in a sample, are examples of concentration techniques. The relationship between the signal and the analyte’s concentration is a theoretical function that depends on experimental conditions and the instrumentation used to measure the signal. For this reason the value of k A in Equation \ref{3.2} is determined experimentally. Since most concentration techniques rely on measuring an optical or electrical signal, they also are known as “instrumental” techniques.