When 174 g of manganese dioxide ( MnO ₂ ) is reacted with 146 g of hydrochloric acid ( HCl ), chlorine gas is evolved along with manganese(II) chloride and water. The mass of the excess reagent left unreacted in grams is _______. (Given molar masses: Mn = 55 g mol ⁻¹ , O = 16 g mol ⁻¹ , H = 1 g mol ⁻¹ , Cl = 35.5 g mol ⁻¹ )

Step-by-step solution

The balanced chemical equation for the reaction is: MnO ₂ + 4 HCl MnCl ₂ + 2 H ₂ O + Cl ₂ Molar mass of MnO ₂ = 55 + 2(16) = 87 g mol ⁻¹ Molar mass of HCl = 1 + 35.5 = 36.5 g mol ⁻¹ Initial moles of MnO ₂ = 174 87 = 2 moles Initial moles of HCl = 146 36.5 = 4 moles To identify the limiting reagent, divide the moles by their respective stoichiometric coefficients: For MnO ₂ : 2 1 = 2 For HCl : 4 4 = 1 Since 1 Moles of MnO ₂ required to react completely with 4 moles of HCl = 1 4 4 = 1 mole Moles of MnO ₂ left unreact