The chemical formula x\\C(i(OH)2] +X2[HNO3] > xj\CA(N03)2] T^4!H2C] indicates that x\

Chapter 6, Problem 11

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The chemical formula x\\C(i(OH)2] +X2[HNO3] > xj\CA(N03)2] T^4!H2C] indicates that x\ molecules of calcium hydroxide Ca(OH)2 combines with X2 molecules of nitric acid HNOy to yield xy molecules of calcium nitrate CA{NOy)2 and X4 molecules of water HyO.lo determine x\,X2,xy, and X4, we set up equations for atoms of calcium Ca, oxygen O, hydrogen H, and nitrogen N. Since the atoms are not destroyed in this chemical reaction, a balanced reaction requires that for calcium X| = Xy, for oxygen 2xi + 3x2 = 6x3 + X4, for hydrogen 2x] + X2 = 2x4, and for nitrogen X2 = 2x3. The resulting linear system Ax = 0 or 10-1 0' X\ "0" 2 3 -6 -1 X2 0 2 1 0-2 Xy 0 0 1 K) O X4 0 a. Compute the determinant of A. b. Why must part (a) give that result? c. Find X|, X2, X3, and X4 to balance the chemical equation. d. Is the answer in part (c) unique?