Vanadium is extracted from (s) by reduction with calcium metal in the presence of…

CHEMISTRY · Multi-part · A Level · Chemistry · Energetics · Energetics

Problem

Vanadium is extracted from V2O5V_2O_5(s) by reduction with calcium metal in the presence of CaCl₂ flux, according to the simplified reaction V2O5V_2O_5(s) →\rightarrow 5 Ca(s) →\rightarrow 2 V(s) + 5 CaO(s) An engineering intern constructed the multi-step enthalpy calculation below to estimate the heat released. Several logical and arithmetic errors are suspected. Step A: V2O5V_2O_5(s) →\rightarrow 2 VO2VO_2(s) + 12 O2\frac{1}{2}\,O_2(g)  ΔH=+204 kJ\Delta H = +204\,\text{kJ} Step B: CaOCaO(s) + 12 O2\frac{1}{2}\,O_2(g) →\rightarrow CaO2CaO_2(s)  ΔH=−150 kJ\Delta H = -150\,\text{kJ} Step C: 2 VO2VO_2(s) + 5 Ca(s) + 5 CaO2CaO_2(s) →\rightarrow 2 V(s) + 5 CaOCaO(s) + 5 CaO2CaO_2(s)  ΔH=−1120 kJ\Delta H = -1120\,\text{kJ} The intern added Steps A–C without any modifications and reported ΔH=−1066 kJ\Delta H = -1066\,\text{kJ} for the target reaction. (1) Part 1: (a) Perform a detailed species inventory after summing Steps A–C exactly as written. Identify every species that erroneously remains uncancelled with its corresponding coefficient. (2) Part 2: (b) Outline a corrected set of manipulations (reversals and/or coefficient adjustments) that would allow complete cancellation of intermediate species while preserving mass balance for O, V, and Ca in the net reaction. (3) Part 3: (c) Recalculate the overall ΔH\Delta H for the extraction of vanadium using your corrected sequence from part (b). Show each intermediate arithmetic step and obtain a final value with appropriate sign and unit. (4) Part 4: (d) Explain why failing to adjust Step B for proper stoichiometry of O2O_2 directly impacts both mass balance and the numerical value of ΔH\Delta H in the overall reaction.

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