The amount of uranium in an ore can be determined by a redox

The amount of uranium in an ore can be determined by a redox back titration. The analysis is accomplished by dissolving the ore in sulfuric acid and reducing the resulting UO22+ to U4+ with a Walden reductor. The resulting solution is treated with an excess of Fe3+, forming Fe2+ and U6+. The Fe2+ is titrated with a standard solution of K2Cr2O7. In a typical analysis a 0.315-g sample of ore is passed through the Walden reductor and treated with 50.00 mL of 0.0125 M Fe3+. Back titrating with 0.00987 M K2Cr2O7 requires 10.52 mL. What is the %w/w U in the sample? The answer is 23.5% but how??

Solution

milimoles of Fe3+ left can be determined from back titration = 0.00987*10.52*6 = 0.623mM;;;;;; 6Fe3+ + 2Cr+6 -------> 6Fe2+ + 2Cr+3;;;;;;;;; total moles of Fe 3+ present = 50*0.125*2 = 1.25;;;;;; 2Fe3+ + U+4 ------> 2Fe2+ + U+6;;;;;;;;; milimoles of Fe 3+ consumed = 1.25 - 0.623 =0.627;;;;;; milimoles of uranium present = 0.627/2 = 0.3135;;;;;;;; wt of uranium = (0.3135 * 236)/100 = 0.073986;;;; w/w = (0.073986/0.315)*100 = 23.5