Strontium metal is responsible for the red color in fireworks. Fireworks manufacturers use strontium carbonate, which can be produced by combining strontium metal, graphite (C), and oxygen gas. The formation of one mole of \(\mathrm{SrCO}_{3}\) releases \(1.220 \times 10^{3} \mathrm{~kJ}\) of energy. (a) Write a balanced thermochemical equation for the reaction. (b) What is \(\Delta H\) when \(10.00 \mathrm{~L}\) of oxygen at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is used by the reaction?

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It involves using balanced chemical equations to calculate the amounts of substances consumed and produced. In the problem, the stoichiometry is used to determine how much strontium carbonate (\r\(\mathrm{SrCO_3}\)) is produced from a specific amount of oxygen gas (\r\(\mathrm{O_2}\)).

\rStoichiometry is crucial because it ensures that the law of conservation of mass is upheld—matter is neither created nor destroyed during a chemical reaction. To perform stoichiometric calculations, a balanced chemical equation is a must as it provides the mole ratio of reactants to products. If you have \r\(\frac{3}{2}\) moles of \r\(\mathrm{O_2}\), you will get 1 mole of \r\(\mathrm{SrCO_3}\), as indicated by the coefficients in the balanced thermochemical equation. These coefficients act as conversion factors that allow us to move from moles of one substance to moles of another.

Key to Stoichiometry

Understanding stoichiometry involves three main steps: identifying the correct balanced equation, using molar ratios to convert between substances, and ensuring that units are consistent to get the final answer accurately. For a deeper understanding, always make sure to practice with various equations and consider the limiting reactant which determines the maximum amount of product that can be formed in a reaction.

Enthalpy change, denoted as \r\(\Delta H\), is the amount of heat absorbed or released during a chemical reaction at constant pressure. In most cases, a negative \r\(\Delta H\) value indicates an exothermic reaction, where heat is released into the surroundings, while a positive value signifies an endothermic reaction, where heat is absorbed from the surroundings.

\rEnthalpy change is an essential concept in thermochemistry because it indicates the energy transfer as heat, which accompanies chemical reactions. In the exercise given, \r\(\Delta H\) helps us understand how much energy is released when a specified quantity of strontium carbonate is formed. With 1 mole of \r\(\mathrm{SrCO_3}\) releasing \r\(1.220 \times 10^3 \mathrm{~kJ}\) of energy, this information, along with the amount of \r\(\mathrm{SrCO_3}\) formed (calculated using stoichiometry), allows for the determination of the total energy change for the reaction.

Practical Example

This concept is widely applied in various scientific fields, such as calculating the energy changes in biochemical reactions, determining the amount of heat required to warm a substance, or even in designing industrial processes that need to be energy-efficient.

The ideal gas law is a fundamental equation that relates the pressure, volume, temperature, and amount of moles of a gas. Expressed as \r\(PV = nRT\), where \r\(P\) is the pressure, \r\(V\) is the volume, \r\(n\) is the number of moles, \r\(R\) is the ideal gas constant, and \r\(T\) is the temperature in Kelvin. This law assumes gases behave ideally, meaning the particles have no volume and experience no interparticle forces.

\rIn the exercise, the Ideal Gas Law is used to calculate the moles of oxygen gas used in the reaction, essential for applying stoichiometry to find the required quantities. The ability to manipulate the Ideal Gas Law equation and apply it practically allows for the determination of any one variable as long as the others are known.

Applying the Law

To use the Ideal Gas Law, conversion of units to the correct SI units is important, such as temperature to Kelvin and volume to liters. Moreover, it's important to note that the Ideal Gas Law is an approximation that works best under low pressure and high temperature conditions, where gases tend to behave more ideally.