(a) Consider the combustion of ethylene, \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\) \(3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) .\) If the concentration of \(\mathrm{C}_{2} \mathrm{H}_{4}\) is decreasing at the rate of \(0.036 \mathrm{M} / \mathrm{s},\) what are the rates of change in the concentrations of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} ?(\mathbf{b})\) The rate of decrease in \(\mathrm{N}_{2} \mathrm{H}_{4}\) partial pressure in a closed reaction vessel from the reaction \(\mathrm{N}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)\) is 74 torr per hour. What are the rates of change of \(\mathrm{NH}_{3}\) partial pressure and total pressure in the vessel?

Understanding reaction stoichiometry is pivotal for analyzing most chemical reactions, including the calculation of reaction rates. Stoichiometry involves the quantitative relationship between the amounts of reactants and products in a chemical reaction. It's anchored in the balanced chemical equation which provides the mole ratios of the substances involved.

Consider the combustion of ethylene given in the exercise. The balanced equation, \(\mathrm{C}_{2}\mathrm{H}_{4}(g)+3\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{CO}_{2}(g)+2\mathrm{ H}_{2}\mathrm{O}(g)\),indicates that 1 mole of ethylene reacts with 3 moles of oxygen to produce 2 moles of carbon dioxide and 2 moles of water. These ratios are used to determine how changes in the concentration of one species will affect the concentration of others. For example, if the concentration of ethylene decreases, the concentrations of carbon dioxide and water will increase, which can be expressed with specific rate relationships based on stoichiometry.

Ethylene combustion is a chemical reaction where ethylene (\(\mathrm{C}_{2}\mathrm{H}_{4}\)) reacts with oxygen (\(\mathrm{O}_{2}\)) to form carbon dioxide (\(\mathrm{CO}_{2}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). This process is an example of a combustion reaction, a type of exothermic reaction that releases energy, mainly in the form of heat and sometimes light.

In such reactions, it's crucial to monitor the rate at which the reactants are consumed and the products are formed, which not only affects the energy release but also the control of the reaction process. The reaction rate can be manipulated by various factors such as concentration, temperature, and presence of a catalyst. For instance, as the exercise states, the rate at which the concentration of ethylene decreases is -0.036 M/s, which can be used to calculate the rate of formation of the products using the stoichiometry of the balanced equation.

The rate of a reaction refers to the speed at which reactants are converted into products. This rate can be expressed in terms of the change in concentration of a reactant or product over a certain time period. In the exercise, the rate of ethylene concentration decrease is given, and using the stoichiometric coefficients from the balanced equation, the rates of formation for carbon dioxide and water can be deduced.

For a reaction like ethylene combustion, the rate will determine the amount of heat and light energy produced per unit of time, which is essential for safety and efficiency in industrial processes. Understanding the factors that influence the reaction rate, which include the nature of the reactants, surface area, temperature, concentration, and presence of catalysts, is fundamental for controlling and optimizing chemical reactions.

In gas-phase reactions, partial pressure is a measure of the pressure contributed by a specific gas in a mixture of gases. Modification in partial pressure reflects changes in gas concentration. When chemical reactions occur in a closed system, like the decomposition of hydrazine (\(\mathrm{N}_{2}\mathrm{H}_{4}\)), as described in the exercise, the rates of partial pressure changes for each gas can be calculated.

The exercise showcases how stoichiometry dictates the change in partial pressure of ammonia (\(\mathrm{NH}_{3}\)) based on the change in partial pressure of hydrazine. Due to the stoichiometric relationship, a 74 torr/h decrease in hydrazine results in a 148 torr/h increase of ammonia. Nonetheless, since the reaction does not result in a net change in the amount of gas (molecules are neither created nor destroyed, only rearranged), the total pressure in the vessel remains unchanged, demonstrating another essential aspect of chemical reactions: conservation of mass in a closed system.