Analytical Chem istry - DePauw University

80 Analytical Chemistry 2.0Table 4.10 Propagation of Uncertainty for SelectedMathematical Functions †Functionu RR = kAu = kuRAR = A+ Bu = u + u2 2R A BR = A−Bu = u + u2 2R A BR = A×BRA=BuRuR2 2u u= ⎛ ⎞⎝⎜A ⎠⎟ +⎛ ⎞⎝⎜B ⎠⎟R A B2 2u u= ⎛ ⎞⎝⎜A ⎠⎟ +⎛ ⎞⎝⎜B ⎠⎟R A BR = ln( A) uR = log( A) uRRuA=A= 0.4343×uAARA= euRR= uARA= 10uRR= 2.303×uA4C.5 Uncertainty for Other Mathematical FunctionsMany other mathematical operations are common in analytical chemistry,including powers, roots, and logarithms. Table 4.10 provides equations forpropagating uncertainty for some of these function.Example 4.8R =A kIf the pH of a solution is 3.72 with an absolute uncertainty of ±0.03, whatis the [H + ] and its uncertainty?uRRuA= k ×A† Assumes that the measurements A and B are independent; k is a constant whose value has nouncertainty.