portable hot packs are available for skiers and other people engaged in other outdoor activities in a cold…

portable hot packs are available for skiers and other people engaged in other outdoor activities in a cold climate. the air - permeable paper packet contains a mixture of powdered iron, sodium chloride, and other components, all moistened by a little water. the exothermic reaction that produces the heat is a very common one, the rusting of iron: 4fe(s)+3o₂(g)→2fe₂o₃(s). when the outside plastic envelope is removed, o₂ molecules penetrate the paper, causing the reaction to begin. a particular packet contains 200. g of iron to warm your hands or feet for up to 4 hours. calculate the amount of heat (in kj) associated with this reaction. be sure your answer has the correct number of significant digits. note: reference the thermodynamic properties of pure substances table for additional information.

portable hot packs are available for skiers and other people engaged in other outdoor activities in a cold climate. the air - permeable paper packet contains a mixture of powdered iron, sodium chloride, and other components, all moistened by a little water. the exothermic reaction that produces the heat is a very common one, the rusting of iron: 4fe(s)+3o₂(g)→2fe₂o₃(s). when the outside plastic envelope is removed, o₂ molecules penetrate the paper, causing the reaction to begin. a particular packet contains 200. g of iron to warm your hands or feet for up to 4 hours. calculate the amount of heat (in kj) associated with this reaction. be sure your answer has the correct number of significant digits. note: reference the thermodynamic properties of pure substances table for additional information.

Answer

Explanation:

Step1: Calculate moles of iron

The molar mass of iron ($Fe$) is $M_{Fe}=55.85\ g/mol$. The number of moles of iron $n_{Fe}$ is calculated using the formula $n=\frac{m}{M}$, where $m = 200\ g$. So $n_{Fe}=\frac{200\ g}{55.85\ g/mol}\approx3.5828\ mol$.

Step2: Determine heat - reaction relationship

From the balanced chemical equation $4Fe(s)+3O_2(g)\to2Fe_2O_3(s)$, the standard enthalpy of formation of $Fe_2O_3(s)$ is $\Delta H_f^{\circ}(Fe_2O_3)= - 824.2\ kJ/mol$. The enthalpy change for the reaction $\Delta H_{rxn}$ is calculated as follows: $\Delta H_{rxn}=2\Delta H_f^{\circ}(Fe_2O_3)-[4\Delta H_f^{\circ}(Fe)+3\Delta H_f^{\circ}(O_2)]$. Since $\Delta H_f^{\circ}(Fe) = 0\ kJ/mol$ and $\Delta H_f^{\circ}(O_2)=0\ kJ/mol$, $\Delta H_{rxn}=2\times(- 824.2\ kJ/mol)=-1648.4\ kJ/mol$ for the reaction as written (for 4 moles of $Fe$).

Step3: Calculate heat for given amount of iron

Let $q$ be the heat released. We know that the heat released is proportional to the number of moles of iron reacted. The ratio of moles of iron in our sample to the moles of iron in the balanced - equation is used to find $q$. If 4 moles of $Fe$ release $1648.4\ kJ$ of heat, then for $n_{Fe}=3.5828\ mol$ of $Fe$, we use the proportion $\frac{q}{n_{Fe}}=\frac{\Delta H_{rxn}}{4\ mol}$. So $q=\frac{3.5828\ mol\times1648.4\ kJ}{4\ mol}\approx1.48\times10^{3}\ kJ$.

Answer:

$1.48\times 10^{3}\ kJ$