Question

You are given the following reactions at \(25^{\circ} \mathrm{C}: 2 \mathrm{NaHCO}_{3}(\mathrm{~s})\) \(\rightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{~s}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\ell), \Delta \mathrm{H}=30.92 \mathrm{Kcal} / \mathrm{mole}\) \(\Delta \mathrm{H}^{\circ} \mathrm{Na} 2 \operatorname{CO} 3(\mathrm{~s})=-270.3 \cdot \Delta \mathrm{H}^{\circ} \mathrm{CO} 2(\mathrm{~g})=-94.0\) and \(\Delta \mathrm{H}^{\circ} \mathrm{H}_{2} \mathrm{O}(\ell)\) \(=-68.4 \mathrm{Kcal} / \mathrm{mole}\), what is the standard enthalpy of formation for \(\mathrm{NaHCO}_{3}(\mathrm{~s})\) ?

Short answer

The standard enthalpy of formation for sodium bicarbonate (\( \mathrm{NaHCO}_{3}(\mathrm{~s}) \)) is 463.62 Kcal/mol.

Step-by-step solution

Understand the Hess' Law equation

The equation for Hess' Law is: \[ \Delta H_{total} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \ldots + \Delta H_n \] Where \( \Delta H_{total} \) is the total enthalpy change for the chemical reaction, and \( \Delta H_1, \Delta H_2, \Delta H_3, \ldots, \Delta H_n \) are the enthalpy changes for individual steps in the reaction.

Identify known and unknown values

The standard enthalpy of formation for sodium bicarbonate (\( \Delta H^{\circ}_{formation \, NaHCO_3} \)) is the unknown value. The known values include the enthalpy for the decomposition reaction (\( \Delta H = 30.92 \, \mathrm{Kcal} / \mathrm{mole} \)) and the standard enthalpies of formation for sodium carbonate (\( \Delta H^{\circ}_{Na_2CO_3} = -270.3 \, \mathrm{Kcal} / \mathrm{mole} \)), carbon dioxide (\( \Delta H^{\circ}_{CO_2} = -94.0 \, \mathrm{Kcal} / \mathrm{mole} \)), and water (\( \Delta H^{\circ}_{H_2O} = -68.4 \, \mathrm{Kcal} / \mathrm{mole} \)).

Apply Hess' Law

Formulate the equation, using Hess' Law. \[ \Delta H^{\circ}_{formation \, NaHCO_3} = \Delta H - \left( \Delta H^{\circ}_{Na_2CO_3} + \Delta H^{\circ}_{CO_2} + \Delta H^{\circ}_{H_2O} \right) \] Plugging in the known values: \[ \Delta H^{\circ}_{formation \, NaHCO_3} = 30.92 - \left( -270.3 -94.0 -68.4 \right) \]

Evaluate the equation

By calculating the result, find the enthalpy of formation for sodium bicarbonate: \[ \Delta H^{\circ}_{formation \, NaHCO_3} = 30.92 - \left( -432.7 \right) = 463.62 \, \mathrm{Kcal} / \mathrm{mole} \] So the standard enthalpy of formation for sodium bicarbonate (\( \mathrm{NaHCO}_{3}(\mathrm{~s}) \)) is 463.62 Kcal/mol.

Key concepts

Hess' Law

Hess' Law is a fundamental principle in thermochemistry named after the Swiss chemist Germain Hess. It states that the total enthalpy change during a chemical reaction is the same, no matter how many steps the reaction is carried out in. In simpler terms, if a reaction can be expressed as the sum of two or more steps, the heat change for the entire process is equal to the sum of the enthalpy changes for each step. This concept is exceedingly helpful when we cannot directly measure the enthalpy change of a reaction. Instead, we piece together known enthalpy changes of related reactions.

Our ability to calculate unknown enthalpy changes, such as the standard enthalpy of formation for a compound, is made possible through Hess' Law. By rearranging and combining known thermochemical equations, we can deduce the enthalpy change for the overall chemical reaction. This application of Hess' Law enables students and scientists to calculate the energetics of reactions that would otherwise be difficult to ascertain.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the energy changes involved in chemical reactions. Fundamentally, it looks at the heat absorbed or released during these processes, which is a form of energy known as enthalpy (\( \text{H} \)). The key to understanding thermochemistry is grasping that energy is conserved in all chemical reactions. This means that any heat lost or gained in a reaction must be accounted for, whether it transforms into another type of energy or transfers to the surroundings.

Importance of Standard Conditions

Thermochemical measurements are often made under standard conditions (usually 25 degrees Celsius and 1 atmosphere of pressure), which makes it easier to compare and compile data across various reactions and substances. The 'standard enthalpy of formation' is a crucial concept in thermochemistry. It represents the heat change that occurs when one mole of a compound is formed from its elements in their standard states.

Enthalpy Changes

Enthalpy changes convey the heat energy that is taken in or given off during a chemical reaction while the pressure is kept constant. It's represented as \( \text{H} \) and measured in kilocalories or joules per mole. There are different types of enthalpy changes: formation, reaction, combustion, to name a few, with formation being a main focus in our discussion.

Signs indicate the reaction type - for instance, a negative enthalpy change (exothermic reaction) means heat is released to the surroundings, whereas a positive change (endothermic reaction) indicates heat is absorbed. This understanding provides insight into the energy dynamics of reactions and can be fundamental in fields like material science, environmental chemistry, and engineering where energy efficiency and control are paramount.

Chemical Reactions

Chemical reactions involve the breaking and forming of chemical bonds, resulting in the transformation of substances into new products. The bonds between atoms in molecules store energy, and when these bonds break or form during a reaction, energy is either released or consumed.

Role of Energy in Reactions

Reactants need a specific amount of energy to initiate a reaction, called the activation energy. When a chemical reaction occurs, the difference in the energy content between reactants and products results in an enthalpy change. This can be visualized as the reaction's energy landscape, with the energy change causing a 'shift' in the landscape. Understanding these changes and the factors that affect reaction rates, such as temperature, pressure, and catalysts, is essential in controlling and applying chemical reactions in industry and research.