Thermogravimetric analysis and propagation of error.12 Crystals of deuterated potassium dihydrogen phosphate, K(DxH1 - x)2PO4, are used in optics as a light valve, as a light deflector, and for frequency doubling of lasers. The optical properties are sensitive to the fraction of deuterium in the material. A publication states that deuterium content can be determined by measuring the mass lost by dehydration of the crystal after slow heating to 450°C in a Pt crucible under N2.

(a) Let be the mass of product divided by the mass of reactant:

Show that the coefficient x in K(DxH1-x)2PO4 is related to by the equation

What would be the value of if starting material were 100% deuterated?
(b) One crystal measured in triplicate gave an average value of α = 0.856 77. Find x for this crystal.
(c) From Equation C.1 in Appendix C, show that the uncertainty in x (ex) is related to the uncertainty in (e) by the equation.

(d) The uncertainty in deuterium:hydrogen stoichiometry is ex. The authors estimate that their uncertainty in is eα =0.000 1. From e, compute ex. Write the stoichiometry in the form x (ex). If e were 0.001 (which is perfectly reasonable), what would ex be?

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450 C FM 136.085 3+2.012 55x FM 118.070 3 mass of KPO mass of K(D,H-2PO4 58.667 0 67.618 3 x = 58.667 0