Problem 101 - Chemistry: The Central Science

Question

The standard heats of formation of \(\mathrm{H}_{2} \mathrm{O}(g), \mathrm{H}_{2} \mathrm{~S}(g), \mathrm{H}_{2} \mathrm{Se}(g)\), and \(\mathrm{H}_{2} \mathrm{Te}(g)\) are \(-241.8,-20.17,+29.7\), and \(+99.6 \mathrm{~kJ} /\) mol, respectively. The enthalpies necessary to convert the elements in their standard states to one mole of gaseous atoms are \(248,277,227\), and \(197 \mathrm{~kJ} / \mathrm{mol}\) of atoms for \(\mathrm{O}, \mathrm{S}, \mathrm{Se}\), and Te, respectively. The enthalpy for dissociation of \(\mathrm{H}_{2}\) is \(436 \mathrm{~kJ} / \mathrm{mol}\). Calculate the average \(\mathrm{H}-\mathrm{O}, \mathrm{H}-\mathrm{S}, \mathrm{H}-\mathrm{Se}\), and \(\mathrm{H}\) - Te bond enthalpies, and comment on their trend.

Step-by-Step Solution

Answer

In summary, the average bond enthalpies for H-O, H-S, H-Se, and H-Te are -214.9 kJ/mol, -89.59 kJ/mol, -89.65 kJ/mol, and -69.7 kJ/mol, respectively. The bond enthalpy decreases as we move down the group (O, S, Se, and Te) in the periodic table, indicating a decrease in bond strength. This trend can be attributed to the increase in atomic size and the decrease in electronegativity as we move down the group.

Step 1: Calculate Enthalpy Change for Breaking Molecules

Let's first find the total enthalpy change for breaking one mole of each molecule, H2O, H2S, H2Se, and H2Te. To do this, we will use the formula: Enthalpy Change = Enthalpy of Formation + Enthalpy for Breaking Elements - Enthalpy for Dissociation of H2 For each molecule, we will calculate the enthalpy change using the given values for the standard heats of formation, enthalpies to convert the elements to gaseous atoms, and enthalpy for dissociation of H2.

Step 2: Calculate the Average Bond Enthalpies

Now that we have the enthalpy change for breaking one mole of each molecule, we can find the average bond enthalpy for each type of bond (H-O, H-S, H-Se, and H-Te). To do this, we will divide the enthalpy change by the number of bonds of that type in the molecule. Since there are two bonds of each type in the molecules, we can calculate the average bond enthalpy as follows: Average Bond Enthalpy = Enthalpy Change / 2 We will perform this calculation for each molecule to find the average bond enthalpies for H-O, H-S, H-Se, and H-Te.

Step 3: Comment on the Trend

After finding the average bond enthalpies for H-O, H-S, H-Se, and H-Te, we will compare them and comment on any trends observed in these values. Solution:

Step 1: Calculate Enthalpy Change for Breaking Molecules

First, let's calculate the total enthalpy change for breaking one mole of each molecule: For H2O: Enthalpy Change = -241.8 kJ/mol + 248 kJ/mol - 436 kJ/mol = -429.8 kJ/mol For H2S: Enthalpy Change = -20.17 kJ/mol + 277 kJ/mol - 436 kJ/mol = -179.17 kJ/mol For H2Se: Enthalpy Change = 29.7 kJ/mol + 227 kJ/mol - 436 kJ/mol = -179.3 kJ/mol For H2Te: Enthalpy Change = 99.6 kJ/mol + 197 kJ/mol - 436 kJ/mol = -139.4 kJ/mol

Step 2: Calculate the Average Bond Enthalpies

Now, let's calculate the average bond enthalpy for each type of bond: For H-O: Average Bond Enthalpy = (-429.8 kJ/mol) / 2 = -214.9 kJ/mol For H-S: Average Bond Enthalpy = (-179.17 kJ/mol) / 2 = -89.59 kJ/mol For H-Se: Average Bond Enthalpy = (-179.3 kJ/mol) / 2 = -89.65 kJ/mol For H-Te: Average Bond Enthalpy = (-139.4 kJ/mol) / 2 = -69.7 kJ/mol

Step 3: Comment on the Trend

By comparing the average bond enthalpies for H-O, H-S, H-Se, and H-Te, we can see that the bond enthalpy decreases as we move down the group (O, S, Se, and Te) in the periodic table. This indicates that the strength of the bond decreases as we move down the group. The decrease in bond strength can be attributed to the increase in atomic size and the decrease in electronegativity as we move down the group.

Key Concepts

Enthalpy Change

Enthalpy change is a concept in chemistry that refers to the amount of energy absorbed or released during a chemical reaction at constant pressure. It is an important measure because it helps us understand how energy is transferred in reactions. The formula used for calculating enthalpy change in bonding analysis involves three components:

• The standard heat of formation, which indicates the energy change when a compound forms from its elements.
• The energy required to convert elements from their standard states to gaseous atoms, often referred to as atomization energy.
• The energy required to dissociate a molecule, like splitting a hydrogen molecule into atoms.

To find the total enthalpy change for a compound like water, sulfur dioxide, etc., you sum the standard heat of formation with the atomization energy, and subtract the dissociation energy of any bonds formed, such as H-H bonds. This calculation gives a comprehensive view of the energy changes involved in breaking and forming bonds.

Standard Heats of Formation

Standard heats of formation refer to the enthalpy change when one mole of a compound forms from its elements in their standard states. This concept is fundamental in thermochemistry as it allows us to measure the stability and energy content of a compound. The values are expressed usually in kilojoules per mole (kJ/mol) and can be positive or negative:

• A negative value indicates that energy is released during the formation, implying that the compound is relatively stable.
• A positive value suggests energy absorption, indicating a less stable compound, as seen in some compounds like hydrogen selenide (H₂Se) and telluride (H₂Te).

Using standard heats of formation, chemists can calculate the overall enthalpy change in reactions, which is critical for understanding reaction dynamics and energy requirements.

Trends in the Periodic Table

Trends in the periodic table provide insights into how different chemical properties evolve across different elements. One noticeable trend related to bond enthalpy is observed in groups of elements from top to bottom. As we move down a group in the periodic table—for example, from oxygen through sulfur, selenium, to tellurium:

• The atomic size tends to increase, which leads to longer and usually weaker bonds.
• The electronegativity decreases, affecting how bonding electrons are shared and often resulting in weaker bonds.

This trend is evident in the decreasing bond enthalpies from H-O to H-Te. The weaker bond strength down the group causes lower energy release when bonds break, affecting the overall enthalpy values.

Average Bond Enthalpies

Average bond enthalpies are useful for estimating the strength of covalent bonds in molecules. They provide insight into how much energy is needed to break one mole of a specific type of bond in gaseous molecules. The calculation for average bond enthalpy involves dividing the total enthalpy change by the number of bonds. This value helps in comparing the relative strength of different bonds. For example, in calculating average bond enthalpies for bonds like H-O and H-S, divide the sum of enthalpy changes by the number of such bonds present in the molecular structure. This approach simplifies the understanding of bonding strength across different molecules and highlights noticeable differences, such as stronger H-O bonds compared to H-Te. These differences are not just theoretical; they have practical implications, affecting molecular stability and reactivity, which are vital in fields ranging from materials science to biochemistry.