Question

The vanadium (V) ion in a 0.5000 -g sample of ore is converted to VO \(^{2+}\) ions. The amount of \(\mathrm{VO}^{2+}\) in solution can be determined by reaction with an acid solution of \(\mathrm{KMnO}_{4}\). The balanced equation for the reaction is $$ \begin{array}{r} 5 \mathrm{VO}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+11 \mathrm{H}_{2} \mathrm{O} \longrightarrow \\ \mathrm{Mn}^{2+}(a q)+5 \mathrm{~V}\left(\mathrm{OH}_{4}\right)^{+}(a q)+2 \mathrm{H}^{+}(a q) \end{array} $$ What is the mass percent of vanadium in the ore if \(26.45 \mathrm{~mL}\) of \(0.02250 \mathrm{M}\) permanganate solution is required for complete reaction? 51\. Hydrogen gas is bubbled into a solution of barium hydroxide that has sulfur in it. The equation for the reaction that takes place is $$ \mathrm{H}_{2}(g)+\mathrm{S}(s)+2 \mathrm{OH}^{-}(a q) \longrightarrow \mathrm{S}^{2-}(a q)+2 \mathrm{H}_{2} \mathrm{O} $$ What volume of \(0.349 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) is required to react completely with \(3.00 \mathrm{~g}\) of sulfur?

Short answer

Answer: The mass percent of vanadium in the ore is 30.314375 %.

Step-by-step solution

Find moles of permanganate ions reacted with VO2+

Given the volume and concentration of the permanganate solution, we can determine the moles of MnO4- ions reacted. Use the formula: moles of MnO4- = volume * concentration Moles of MnO4- = 26.45 mL * 0.02250 M = 0.000595125 mol

Find moles of VO2+ using stoichiometry of the balanced equation

Using the balanced equation, we can determine the moles of VO2+ ions using the stoichiometric ratios: 5 VO2+(aq) + MnO4-(aq) + 11 H2O -> Mn2+(aq) + 5 V(OH)4+(aq) + 2 H+(aq) From the equation, 1 mol of MnO4- reacts with 5 mol of VO2+. So we need to multiply the moles of MnO4- by 5 to get the corresponding moles of VO2+: Moles of VO2+ = 5 * moles of MnO4- = 5 * 0.000595125 mol = 0.002975625 mol

Calculate mass of vanadium (V) involved in the reaction

Now we know the moles of VO2+ ions in the sample, we can find the mass of vanadium (V) involved in the reaction. The molar mass of vanadium is 50.94 g/mol. Use the formula: Mass of V = moles of VO2+ * molar mass of V Mass of V = 0.002975625 mol * 50.94 g/mol = 0.151571875 g

Calculate the mass percent of vanadium in the ore

We have determined the mass of vanadium in the 0.5000-g ore sample. Now, we can calculate the mass percent of vanadium using the formula: Mass percent = (Mass of V / Mass of ore) * 100 Mass percent = (0.151571875 g / 0.5000 g) * 100 = 30.314375 % The mass percent of vanadium in the ore is 30.314375 %.