Question

Write thermochemical equations for the formation of one mole of the following compounds from the elements in their stable states at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\). (a) acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) (b) nitrogen dioxide \((g)\) (c) lead(II) bromide (s) (d) phosphorus pentachloride \((g)\)

Short answer

Question: Write the thermochemical equations for the formation of the following compounds from their elements in their stable states at 25°C and 1 atm. a) Acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) b) Nitrogen dioxide, \(\mathrm{NO}_{2}(g)\) c) Lead(II) bromide, \(\mathrm{PbBr}_{2}(s)\) d) Phosphorus pentachloride, \(\mathrm{PCl}_{5}(g)\) Answer: a) \(2 \mathrm{C(s)} + \mathrm{H}_{2} \mathrm{(g)} \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)\) b) \(\frac{1}{2} \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g)\) c) \(\mathrm{Pb(s)} + \mathrm{Br}_{2}(l) \rightarrow \mathrm{PbBr}_{2}(s)\) d) \(\mathrm{P(s)} + \frac{5}{2}\mathrm{Cl}_{2}(g) \rightarrow \mathrm{PCl}_{5}(g)\)

Step-by-step solution

Identify the elements and their stable states

Identify the elements in acetylene and their stable states. Acetylene is a molecule composed of 2 carbon atoms and 2 hydrogen atoms. At 25°C and 1 atm, both carbon and hydrogen are in their solid and gaseous states, respectively. Carbon is present in its atomic form as graphite and hydrogen is present as \(\mathrm{H}_{2}(g)\).

Write the thermochemical equation

Write a balanced chemical equation for the formation of one mole of acetylene from its elements in their stable states. \[2 \mathrm{C(s)} + \mathrm{H}_{2} \mathrm{(g)} \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)\] #b) Nitrogen dioxide \((\mathrm{NO}_{2}(g))\)#

Identify the elements and their stable states

Identify the elements in nitrogen dioxide and their stable states. Nitrogen dioxide is a molecule composed of 1 nitrogen atom and 2 oxygen atoms. At 25°C and 1 atm, nitrogen and oxygen are both in their gaseous states. Nitrogen is present as \(\mathrm{N}_{2}(g)\) and oxygen is present as \(\mathrm{O}_{2}(g)\).

Write the thermochemical equation

Write a balanced chemical equation for the formation of one mole of nitrogen dioxide from its elements in their stable states. \[\frac{1}{2} \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow \mathrm{NO}_{2}(g)\] #c) Lead(II) bromide \((\mathrm{PbBr}_{2}(s))\)#

Identify the elements and their stable states

Identify the elements in lead(II) bromide and their stable states. Lead(II) bromide is a compound composed of 1 lead atom and 2 bromine atoms. At 25°C and 1 atm, lead is a solid, and bromine is a liquid, present as \(\mathrm{Br}_{2}(l)\).

Write the thermochemical equation

Write a balanced chemical equation for the formation of one mole of lead(II) bromide from its elements in their stable states. \[\mathrm{Pb(s)} + \mathrm{Br}_{2}(l) \rightarrow \mathrm{PbBr}_{2}(s)\] #d) Phosphorus pentachloride \((\mathrm{PCl}_{5}(g))\)#

Identify the elements and their stable states

Identify the elements in phosphorus pentachloride and their stable states. Phosphorus pentachloride is a molecule composed of 1 phosphorus atom and 5 chlorine atoms. At 25°C and 1 atm, phosphorus is a solid and chlorine is a gas, present as \(\mathrm{Cl}_{2}(g)\).

Write the thermochemical equation

Write a balanced chemical equation for the formation of one mole of phosphorus pentachloride from its elements in their stable states. \[\mathrm{P(s)} + \frac{5}{2}\mathrm{Cl}_{2}(g) \rightarrow \mathrm{PCl}_{5}(g)\]

Key concepts

Chemical Thermodynamics

Chemical thermodynamics is a subfield of physical chemistry that deals with the relationship between heat energy and chemical reactions. It involves studying the transfer of energy and the direction in which chemical reactions occur. One fundamental concept within this field is the understanding of enthalpy (H), which is used to measure the total heat content of a system. Enthalpy changes, denoted by \( \Delta H \), indicate whether a reaction is exothermic (releases heat, \( \Delta H < 0\)) or endothermic (absorbs heat, \( \Delta H > 0\)).

Thermochemical equations are visual representations of chemical reactions that include information about the enthalpy change. For instance, the formation of acetylene from carbon and hydrogen at standard conditions would incorporate the enthalpy change in the equation, serving as an energy profile for the reaction. In a classroom or homework context, when solving exercises like the given ones, students must visualize energy flow alongside the creation and breaking of chemical bonds—a core aspect of thermodynamic analysis.

These equations are crucial for predicting the feasibility of reactions. Reactions with negative enthalpy changes are typically more likely to occur spontaneously, though this is not the only criterion. Both entropy and temperature are also significant factors determining the reaction's spontaneity, as described by Gibbs free energy.

Balanced Chemical Equations

A balanced chemical equation represents a chemical reaction with an equal number of atoms for each element in the reactants and products, conforming to the Law of Conservation of Mass. Writing balanced equations is essential for accurately conveying the quantities of substances that participate in chemical reactions. For example, the formation of nitrogen dioxide from nitrogen and oxygen requires a balanced equation to reflect the stoichiometric conversion of reactant molecules into product molecules.

In the equations provided, coefficients are used to balance the atoms. In nitrogen dioxide's case, the fractional coefficient \( \frac{1}{2} \) for nitrogen is necessary because it aligns with the diatomic nature of nitrogen gas in its stable form, \( N_2(g) \). Such detailed balancing is crucial as it ensures that the physical interpretation of a reaction is clear and quantifiable, thereby allowing the calculation of quantities like the amount of reactant needed or product formed.

For learners, grasping the concept of balancing equations is foundational before approaching more complex topics. It encapsulates not just a mathematical exercise, but a deeper understanding of how individual atoms come together to form new compounds. This straightforward portrayal of chemical processes also sets the stage for the quantitative analysis of reactions, which is inherently tied to the principles of chemical thermodynamics.

Standard State Conditions

Standard state conditions are a set of fixed parameters used to compare thermodynamic data meaningfully. For solid and liquid elements and compounds, the standard state is the most stable form of the element or compound at 1 atmosphere (atm) of pressure and a specified temperature, typically set at \(25^\circ C\) for practicality and consistency in experiments and tabulated chemical data.

Under these conditions, it is implied that gases are in their pure form at exactly 1 atm pressure. For substances present in solution, standard state implies a concentration of exactly 1 M. For example, when discussing the formation of lead(II) bromide, the standard state of lead is a solid, and that of bromine is a liquid, rather than a gas, because bromine exists as a liquid at room temperature and 1 atm of pressure.

The significance of standard state conditions is that they offer a reference point when measuring and comparing thermodynamic quantities like enthalpy, free energy, and entropy. The exercise provided involves forming compounds from elements in their stable states at this specified baseline. As seen for phosphorus pentachloride, this convention facilitates a common understanding and more straightforward communication of physical data and conversion processes across the scientific community. Students must comprehend these concepts to correctly approach thermochemical equations and their practical applications in predicting the conditions of chemical reactions.