Chemistry

Chemistry

Problem

When a strip of magnesium reacts completely with excess hydrochloric acid in 100.0 mL100.0\,\text{mL} of aqueous solution at an initial temperature of 25.0∘C25.0^{\circ}\text{C}, the temperature rises to 31.4∘C31.4^{\circ}\text{C}. (Density of the solution is 1.00 g mL−11.00\,\text{g mL}^{-1} and its specific heat capacity is 4.18 J g−1 ∘C−14.18\,\text{J g}^{-1}\,^{\circ}\text{C}^{-1}.) The molar enthalpy of the reaction is ΔHrxn=−462 kJ mol−1\Delta H_{\text{rxn}} = -462\,\text{kJ mol}^{-1} with respect to magnesium. Approximately how many moles of magnesium reacted? a) 1.2×10−2 mol1.2 \times 10^{-2}\,\text{mol} b) 5.8×10−3 mol5.8 \times 10^{-3}\,\text{mol} c) 2.9×10−3 mol2.9 \times 10^{-3}\,\text{mol} d) 5.8×10−4 mol5.8 \times 10^{-4}\,\text{mol}
Intuitive explanation

This problem connects the heat released by a chemical reaction to the temperature change it causes in a solution. You'll use calorimetry—the principle that heat lost by the reaction equals heat gained by the solution (qrxn=−qsolutionq_{\text{rxn}} = -q_{\text{solution}})—then relate that heat to moles using the given enthalpy of reaction. Calculate the solution's heat absorption from mass, specific heat, and ΔT\Delta T, then work backward to find moles of Mg.

Intuitive explanation

This problem connects the heat released by a chemical reaction to the temperature change it causes in a solution. You'll use calorimetry—the principle that heat lost by the reaction equals heat gained by the solution (qrxn=−qsolutionq_{\text{rxn}} = -q_{\text{solution}})—then relate that heat to moles using the given enthalpy of reaction. Calculate the solution's heat absorption from mass, specific heat, and ΔT\Delta T, then work backward to find moles of Mg.

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