Problem 43 - Chemistry: The Central Science

Question

Consider the following reaction: $$ 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) \quad \Delta H=-1204 \mathrm{~kJ} $$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when \(3.55 \mathrm{~g}\) of \(\mathrm{Mg}(s)\) reacts at constant pressure. (c) How many grams of \(\mathrm{MgO}\) are produced during an enthalpy change of \(-234 \mathrm{~kJ}\) ? (d) How many kilojoules of heat are absorbed when \(40.3 \mathrm{~g}\) of \(\mathrm{MgO}(s)\) is decomposed into \(\mathrm{Mg}(s)\) and \(\mathrm{O}_{2}(g)\) at constant pressure?

Step-by-Step Solution

Answer

(a) The reaction is exothermic since \(\Delta H = -1204 \mathrm{~kJ}\) is negative. (b) The amount of heat transferred when \(3.55 \mathrm{~g}\) of Mg reacts at constant pressure is \(-88.1 \mathrm{~kJ}\). (c) \(15.6 \mathrm{~g}\) of MgO are produced during an enthalpy change of \(-234 \mathrm{~kJ}\). (d) \(602 \mathrm{~kJ}\) of heat are absorbed when \(40.3 \mathrm{~g}\) of MgO is decomposed into Mg and O2 at constant pressure.

Step 1: (a) Identify Reaction Type:

To determine if the reaction is exothermic or endothermic, we need to look at the value of the enthalpy change during the reaction, which is given as \(\Delta H = -1204 \mathrm{~kJ}\). A negative value of \(\Delta H\) indicates that the reaction releases heat, making it an exothermic reaction.

Step 2: (b) Calculate Heat Transferred:

First, we need to find the molar mass of magnesium, which is found to be 24.305 g/mol by checking a periodic table. Then, we will determine the moles of magnesium that reacted, and use the stoichiometry of the balanced chemical equation to find the heat transferred. 1. Find the moles of Mg that reacted: Moles of Mg = (mass of Mg) / (molar mass of Mg) = (3.55 g) / (24.305 g/mol) = 0.146 mol Mg 2. Use stoichiometry to find the heat released: Moles of heat = 2 moles of Mg -> -1204 kJ Moles of heat = 0.146 moles of Mg -> x kJ x = (0.146 mol Mg) * (-1204 kJ) / (2 mol Mg) = -88.1 kJ So, the amount of heat transferred when 3.55 g of Mg reacts at constant pressure is -88.1 kJ.

Step 3: (c) Calculate Mass of MgO Produced:

In this problem, we are given the enthalpy change and need to find the mass of MgO produced. Using the balanced chemical equation and the molar mass of MgO, we can find the mass of MgO produced. 1. Use stoichiometry to find the moles of MgO produced: Enthalpy change = 2 moles of MgO -> -1204 kJ Enthalpy change = x moles of MgO -> -234 kJ x = ( -234 kJ) * (2 mol MgO) / (-1204 kJ) = 0.388 mol MgO 2. Find the mass of MgO produced: Molar mass of MgO = 40.305 g/mol Mass of MgO = (moles of MgO) * (molar mass of MgO) = (0.388 mol MgO) * (40.305 g/mol) = 15.6 g So, 15.6 g of MgO are produced during an enthalpy change of -234 kJ.

Step 4: (d) Calculate Heat Absorbed:

In this problem, we are given the mass of MgO decomposed and need to find the heat absorbed. Using the balanced chemical equation, we can find the heat absorbed. 1. Find the moles of MgO decomposed: Moles of MgO = (mass of MgO) / (molar mass of MgO) = (40.3 g) / (40.305 g/mol) = 1.00 mol MgO 2. Use stoichiometry to find the heat absorbed: Enthalpy change = 2 moles of MgO -> -1204 kJ Enthalpy change = 1.00 mole of MgO -> x kJ x = (1.00 mol MgO) * (-1204 kJ) / (2 mol MgO) = +602 kJ Note that this value is positive because the reaction is reversed. In this case, the reaction is endothermic when going in the reverse direction. So, 602 kJ of heat are absorbed when 40.3 g of MgO is decomposed into Mg and O2 at constant pressure.