Question

Write thermochemical equations for the decomposition of one mole of the following compounds into the elements in their stable states at \(25^{\circ} \mathrm{C}\) and 1 atm. (a) ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) (b) sodium fluoride \((s)\) (c) magnesium sulfate \((s)\) (d) ammonium nitrate \((s)\)

Short answer

Question: Write the balanced thermochemical equation for the decomposition of the following compounds into their elements at 25°C and 1 atm: (a) Ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) (b) Sodium fluoride \((s)\) (c) Magnesium sulfate \((s)\) (d) Ammonium nitrate \((s)\) Answer: (a) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) \rightarrow 2 \mathrm{C}(s) + 3 \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g)\) (b) \(\mathrm{NaF}(s) \rightarrow \mathrm{Na}(s) + \frac{1}{2} \mathrm{F}_{2}(g)\) (c) \(\mathrm{MgSO}_{4}(s) \rightarrow \mathrm{Mg}(s) + \mathrm{S}(s) + 2 \mathrm{O}_{2}(g)\) (d) \(\mathrm{NH}_{4}\mathrm{NO}_{3}(s) \rightarrow \frac{3}{2} \mathrm{N}_{2}(g) + 2 \mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-step solution

Case (a): Ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\)

Ethyl alcohol, also known as ethanol, has the chemical formula \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). The elements involved in the compound are carbon (C), hydrogen (H), and oxygen (O). At 25°C and 1 atm, their stable states are: carbon as a solid (graphite), hydrogen as a gas, and oxygen as a gas. To write the decomposition reaction, balance the equation with respect to the number of atoms of each element on both sides. The balanced thermochemical equation for the decomposition of ethanol is: $$\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) \rightarrow 2 \mathrm{C}(s) + 3 \mathrm{H}_{2}(g) + \frac{1}{2} \mathrm{O}_{2}(g)$$

Case (b): Sodium fluoride \((s)\)

Sodium fluoride has the chemical formula \(\mathrm{NaF}\). The elements involved in the compound are sodium (Na) and fluorine (F). At 25°C and 1 atm, their stable states are: sodium as a solid and fluorine as a gas. To write the decomposition reaction, balance the equation with respect to the number of atoms of each element on both sides. The balanced thermochemical equation for the decomposition of sodium fluoride is: $$\mathrm{NaF}(s) \rightarrow \mathrm{Na}(s) + \frac{1}{2} \mathrm{F}_{2}(g)$$

Case (c): Magnesium sulfate \((s)\)

Magnesium sulfate has the chemical formula \(\mathrm{MgSO}_{4}\). The elements involved in the compound are magnesium (Mg), sulfur (S), and oxygen (O). At 25°C and 1 atm, their stable states are: magnesium as a solid, sulfur as a solid, and oxygen as a gas. To write the decomposition reaction, balance the equation with respect to the number of atoms of each element on both sides. The balanced thermochemical equation for the decomposition of magnesium sulfate is: $$\mathrm{MgSO}_{4}(s) \rightarrow \mathrm{Mg}(s) + \mathrm{S}(s) + 2 \mathrm{O}_{2}(g)$$

Case (d): Ammonium nitrate \((s)\)

Ammonium nitrate has the chemical formula \(\mathrm{NH}_{4}\mathrm{NO}_{3}\). The elements involved in the compound are nitrogen (N), hydrogen (H), and oxygen (O). At 25°C and 1 atm, their stable states are: nitrogen as a gas, hydrogen as a gas, and oxygen as a gas. To write the decomposition reaction, balance the equation with respect to the number of atoms of each element on both sides. The balanced thermochemical equation for the decomposition of ammonium nitrate is: $$\mathrm{NH}_{4}\mathrm{NO}_{3}(s) \rightarrow \frac{3}{2} \mathrm{N}_{2}(g) + 2 \mathrm{H}_{2} \mathrm{O}(g)$$

Key concepts

Chemical Decomposition

Chemical decomposition is the process where a chemical compound breaks down into simpler substances, which are often elements in their most stable forms. In the context of the textbook exercise, decomposition refers to the breaking down of compounds like ethyl alcohol and magnesium sulfate into elements like carbon, oxygen, and sulfur under standard conditions, which is typically at room temperature (25°C) and 1 atmosphere of pressure.

The formula for decomposition reactions can usually be written as: $$\text{AB} \rightarrow \text{A} + \text{B}$$
where AB represents the compound and A and B are the elements or simpler compounds it decomposes into. For a decomposition to occur, energy might need to be supplied, such as heat, to break the chemical bonds in the compound. This process is important not only in laboratory reactions but also in many natural processes, including the breakdown of organic matter.

Stoichiometry

Stoichiometry is the field of chemistry that deals with the quantitative relationships of the reactants and products in a chemical reaction. It is based on the conservation of mass where the total mass of the reactants equals the total mass of the products.

Using stoichiometry, we balance chemical equations to ensure that the number of atoms for each element is the same on both sides of the equation. For example, in the ethanol decomposition reaction:$$\text{C}_2\text{H}_5\text{OH(l)} \rightarrow 2\text{C(s)} + 3\text{H}_2\text{(g)} + \frac{1}{2}\text{O}_2\text{(g)}$$
the stoichiometry tells us that one molecule of ethanol decomposes into two atoms of carbon, three molecules of hydrogen gas, and half a molecule of oxygen gas. This balance is crucial for predicting the amounts of products formed from given amounts of reactants.

Chemical Equilibrium

Chemical equilibrium occurs in a reversible chemical reaction when the rate of the forward reaction equals the rate of the backward reaction, and the concentrations of the reactants and products remain constant over time. At this point, both reactions are occurring, but there is no net change in the amounts of substances.

In some decomposition reactions, the products can recombine to form the original compounds, potentially reaching an equilibrium state. However, the reactions provided in the exercise represent complete decomposition where the reactants fully convert into products and do not recombine, thus equilibrium in this context refers more generally to the idea of a balanced state required to write the reaction correctly.

Enthalpy

Enthalpy is a measure of the heat content of a system at constant pressure and is denoted by the symbol H. In thermochemical reactions, the change in enthalpy, $$\text{ΔH}$$, indicates whether heat is absorbed or released during the reaction.

Thermochemical equations include the enthalpy change as part of the equation, showing the energetic nature of the reaction. For example, a positive $$\text{ΔH}$$ means that the reaction is endothermic and absorbs heat from the surroundings, whereas a negative $$\text{ΔH}$$ indicates that the reaction is exothermic and releases heat. In the exercise solutions, the enthalpy change would be included alongside the balanced equations to provide a complete picture of the thermal characteristics of the decomposition reactions.