Question

In each of the following processes, is any work done when the reaction is carried out at constant pressure in a vessel open to the atmosphere? If so, is work done by the reacting system or on it? (a) Neutralization of \(\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq})\) by \(\mathrm{HCl}(\mathrm{aq}) ;\) (b) conversion of gaseous nitrogen dioxide to gaseous dinitrogen tetroxide; (c) decomposition of calcium carbonate to calcium oxide and carbon dioxide gas.

Short answer

For (a) No work is done. For (b) Work is done on the system. For (c) Work is done by the system.

Step-by-step solution

Identify if work is done (a)

The first process is the reaction between Barium hydroxide and Hydrogen Chloride. The chemical reaction is: \[ \mathrm{Ba(OH)_2(aq) + 2HCl(aq) \longrightarrow BaCl_2(aq) + 2H_2O(l)}\]. It is noticeable that there are no gases at any stage of this reaction, hence no volume change. Consequently, no work is done in this case.

Identify if work is done (b)

The second process is the conversion of nitrogen dioxide to dinitrogen tetroxide. The chemical reaction is: \[ \mathrm{2NO_2(g) \longrightarrow N_2O_4(g)}\]. In this case, there is a reduction in the number of moles of gas (from 2 moles of NO2 to 1 mole of N2O4), indicating a decrease in volume at constant pressure, so work is done on the system.

Identify if work is done (c)

The third process is the decomposition of calcium carbonate to calcium oxide and carbon dioxide gas. The chemical reaction is: \[ \mathrm{CaCO_3(s) \longrightarrow CaO(s) + CO_2(g)}\]. Since there's an increase in the number of moles of gas (from no gaseous reactant to 1 mole of CO2 product), this indicates an increase in volume at constant pressure, so the work is done by the system.

Key concepts

Constant Pressure Processes

Constant pressure processes, also known as isobaric processes, are chemical reactions or physical changes that occur under a constant pressure. This is a common scenario in many laboratory and natural settings, like reactions open to the atmosphere.
In these processes, pressure remains steady while other state variables, such as volume or temperature, may change. Due to maintaining stable pressure, energy changes can be traced more directly, simplifying calculations with enthalpy rather than internal energy.
For example, when a reaction occurs in an open vessel, the atmospheric pressure is maintained constant throughout the process. Any work done is generally related to changes in gas volume—the subject of our next sections. It's important to recognize that even if the overall pressure doesn't change, subtleties like expansion or compression might still result in work being done.
When analyzing such reactions, it's crucial to consider the physical states of reactants and products: if there are gases involved, any volume change can do or require work.

Chemical Reactions and Work

Work in the realm of chemistry often involves doing work against the external pressure, especially when dealing with gases. Work is a way to quantify the energy transfer required to either perform or involve energy in a reaction, specifically in terms of volume changes.
In this context, work ( \(w\) ) is calculated using the formula: \(w = -P \, \Delta V\) , where \(P\) is the pressure and \(\Delta V\) is the change in volume. The negative sign indicates that work done by the system (such as gas expansion) on its surroundings is considered negative, while work done on the system (such as gas compression) is positive.
As seen in the examples from our exercise, even if pressure remains constant, volume changes—whether expand or compress—can determine whether work is done. For instance, the conversion of \(2NO_2(g)\) to \(N_2O_4(g)\) leads to a reduction in gas moles, hence work is done on the system. Conversely, if a reaction increases gas moles, as in \(CaCO_3\) decomposing to \(CO_2\) , work is done by the system.
It's these subtle changes that highlight the interrelation of chemical reactions, states of matter, and energy exchange in thermochemical processes.

Gas Volume Change in Reactions

Gas volume change in chemical reactions is a critical factor in determining whether work is done in a constant pressure process. Changes in the number of moles of gas imply a volume change, which is linked to work done by or on the system.
When a chemical reaction at constant pressure results in an increase in the number of gas moles, the system expands, doing work on the surroundings. Conversely, a reaction that decreases gas moles means the system contracts, with work done on it by the surroundings.
For example, in our exercise, the decomposition of calcium carbonate ( \(CaCO_3\) ) results in the production of carbon dioxide gas ( \(CO_2\) ). This reaction increases the volume by producing a gas where none was before, indicating that work is done by the system.
On the other hand, when nitrogen dioxide ( \(NO_2\) ) is converted to dinitrogen tetroxide ( \(N_2O_4\) ), the reaction leads to a decrease in volume as moles of gas are reduced, signifying work done on the system. Understanding these concepts is vital for interpreting the thermodynamic behavior of reactions happening in open systems at constant pressure.