Question

The following table presents the solubilities of several gases in water at \(25^{\circ} \mathrm{C}\) under a total pressure of gas and water vapor of 101.3 kPa. (a) What volume of \(\mathrm{CH}_{4}(g)\) under standard conditions of temperature and pressure is contained in \(4.0 \mathrm{~L}\) of a saturated solution at \(25^{\circ} \mathrm{C} ?\) (b) The solubilities (in water) of the hydrocarbons are as follows: methane \(<\) ethane \(<\) ethylene. Is this because ethylene is the most polar molecule? (c) What intermolecular interactions can these hydrocarbons have with water? (d) Draw the Lewis dot structures for the three hydrocarbons. Which of these hydrocarbons possess \(\pi\) bonds? Based on their solubilities, would you say \(\pi\) bonds are more or less polarizable than \(\sigma\) bonds? (e) Explain why NO is more soluble in water than either \(\mathrm{N}_{2}\) or \(\mathrm{O}_{2} .\) (f) \(\mathrm{H}_{2} \mathrm{~S}\) is more water-soluble than almost all the other gases in table. What intermolecular forces is \(\mathrm{H}_{2} \mathrm{~S}\) likely to have with water? \((\mathbf{g}) \mathrm{SO}_{2}\) is by far the most water-soluble gas in table. What intermolecular forces is \(\mathrm{SO}_{2}\) likely to have with water? $$ \begin{array}{lc} \hline \text { Gas } & \text { Solubility (mM) } \\ \hline \mathrm{CH}_{4} \text { (methane) } & 1.3 \\ \mathrm{C}_{2} \mathrm{H}_{6} \text { (ethane) } & 1.8 \\ \mathrm{C}_{2} \mathrm{H}_{4} \text { (ethylene) } & 4.7 \\ \mathrm{~N}_{2} & 0.6 \\ \mathrm{O}_{2} & 1.2 \\ \mathrm{NO} & 1.9 \\ \mathrm{H}_{2} \mathrm{~S} & 99 \\ \mathrm{SO}_{2} & 1476 \\ \hline \end{array} $$

Short answer

The volume of CH4 in a 4.0 L saturated solution at standard conditions is approximately 116.48 mL. The solubilities of the hydrocarbons are not due to differences in polarity but due to size and increased London dispersion forces in larger molecules. Methane, ethane, and ethylene can have London dispersion forces with water. Methane and ethane have only σ bonds; ethylene has a π bond. NO is more soluble in water than N2 or O2 because it can form stronger London dispersion forces. H2S has dipole-dipole interactions, London dispersion forces, and some weak hydrogen bonds with water, while SO2 has dipole-dipole interactions, London dispersion forces, and hydrogen bonds with water.

Step-by-step solution

(a) Volume of CH4 in a 4.0 L saturated solution

Given, the solubility of CH4 (methane) at 25 degrees Celsius is 1.3 mM. We need to find the volume of CH4 present in a 4.0 L saturated solution at standard conditions of temperature and pressure (STP). Recall that 1 mol of an ideal gas occupies 22.4 L at STP. 1. First, calculate the moles of CH4 dissolved in the 4.0 L saturated solution. Moles of CH4 = (Solubility of CH4) x (Volume of the solution) Moles of CH4 = 1.3 mM × 4.0 L = 5.2 mmol 2. Now, convert the moles of CH4 to volume at STP. Volume of CH4 = (Moles of CH4) x (Molar volume of an ideal gas at STP) Volume of CH4 = 5.2 mmol × 22.4 L/mol = 116.48 mL So, the volume of CH4 under standard conditions of temperature and pressure in a 4.0 L saturated solution at 25 degrees Celsius is approximately 116.48 mL.

(b) Solubilities of hydrocarbons and polarity

The solubilities of the hydrocarbons are as follows: methane < ethane < ethylene. We need to determine if this order is because ethylene is the most polar molecule. Methane (CH4), ethane (C2H6), and ethylene (C2H4) are all nonpolar molecules. They exhibit only London dispersion forces. The difference in solubility, therefore, is not due to differences in polarity but due to size and increased London dispersion forces in larger molecules.

(c) Intermolecular interactions with water

We are asked to determine the possible intermolecular interactions that methane, ethane, and ethylene can have with water. As all three molecules are nonpolar, they cannot form hydrogen bonds or dipole-dipole interactions with water. The only possible type of intermolecular interaction that these hydrocarbons can have with water is the London dispersion forces.

(d) Lewis dot structures and π bonds

We need to determine the Lewis dot structures for methane, ethane, and ethylene and identify which of these hydrocarbons possess π bonds. 1. Methane (CH4): Structurally, methane is a simple tetrahedral molecule with carbon in the center and four hydrogen atoms bonded to it via single (sigma) bonds. 2. Ethane (C2H6): Ethane consists of two carbon atoms bonded to each other with a single (sigma) bond. Each carbon atom is bonded to three hydrogen atoms via single (sigma) bonds. 3. Ethylene (C2H4): Ethylene is a planar molecule consisting of two carbon atoms bonded to each other with a double bond, which includes one sigma bond and one pi bond. Each carbon atom is bound to two hydrogen atoms via single (sigma) bonds. Based on their solubilities, we cannot definitively conclude if π bonds are more or less polarizable than σ bonds, as solubilities are influenced by other factors such as size and the number of atoms as well.

(e) Solubility of NO

Nitric oxide (NO) is more soluble in water than either N2 or O2. This is because NO is a polar molecule capable of forming stronger London dispersion forces with water molecules. In contrast, N2 and O2 are both nonpolar molecules and do not have a significant interaction with the polar water molecules.

(f) Intermolecular forces of H2S and SO2

Both H2S and SO2 are highly soluble in water compared to other gases in the table. 1. Intermolecular forces of H2S with water: H2S is a polar molecule and can form dipole-dipole interactions and London dispersion forces with water molecules. Additionally, although weaker, it can also form some hydrogen bonds with water due to the presence of a sulfur-hydrogen bond and the electronegativity difference between hydrogen and sulfur. 2. Intermolecular forces of SO2 with water: SO2 is a polar molecule and can form strong dipole-dipole interactions and London dispersion forces with water molecules. Moreover, due to the presence of oxygen atoms within the SO2 molecule, it can also form hydrogen bonds with water, significantly increasing its solubility.

Key concepts

Intermolecular Forces

When discussing the solubility of gases in water, it's crucial to understand the nature of intermolecular forces. Intermolecular forces are interactions that occur between molecules, influencing properties like boiling points, melting points, and solubility. These forces vary in strength and type:

• London Dispersion Forces: These are the weakest of the intermolecular forces and exist in all molecules, regardless of whether they are polar or nonpolar. They arise from temporary, random fluctuations in electron density that create instantaneous dipoles.
• Dipole-Dipole Interactions: These forces occur in polar molecules, where permanent dipoles align and attract each other. The interaction strength is proportionate to the polarity of the molecule.
• Hydrogen Bonds: A special, robust type of dipole-dipole interaction, hydrogen bonds occur when a hydrogen atom bonds to highly electronegative atoms like nitrogen, oxygen, or fluorine. These bonds are responsible for unique properties of water, such as its high surface tension and specific heat capacity.

With gases like NO, H\(_2\)S, and SO\(_2\), their increased solubility in water is due to stronger intermolecular forces at play, primarily dipole-dipole interactions and hydrogen bonding.

Lewis Dot Structures

Lewis dot structures are a simple way to represent the valence electron arrangement in molecules. They help us visualize the bonding in molecules, predicting the number of bonds between atoms and if any lone pairs will affect molecule shape and properties.
For methane (CH\(_4\)), the Lewis structure shows a central carbon atom with four single bonds to hydrogen, reflecting its tetrahedral geometry. No lone pairs are present, giving methane its single sigma (σ) bonds.
Moving to ethane (C\(_2\)H\(_6\)), the structure is an extension of methane's, with two carbon atoms bonded to each other and to three hydrogen atoms each. Again, only sigma bonds are present.
In contrast, ethylene (C\(_2\)H\(_4\)) has a double bond between the two carbon atoms, consisting of one sigma and one pi (π) bond. The presence of the π bond makes ethylene unique, contributing to its planar structure and influencing its chemical reactivity. Understanding these differences aids in comprehending how molecular structure impacts properties, like solubility.

Polar and Nonpolar Molecules

Polar and nonpolar molecules behave differently in various environments due to their distribution of electric charges. This polarity drastically affects intermolecular forces and thus solubility.

• Polar Molecules: Has uneven distribution of charge due to differences in electronegativity between bonded atoms. They have permanent dipoles, making them soluble in polar solvents like water. NO and SO\(_2\) are examples, whose polarity leads to stronger dipole-dipole interactions with water.
• Nonpolar Molecules: Charge distribution is even, often because the molecule is symmetrical or the atoms have similar electronegativity. These molecules, like CH\(_4\) and C\(_2\)H\(_6\), interact weakly with polar solvents due to only having London dispersion forces.

While comparing solubility among hydrocarbons, size, and electronic structure, rather than polarity, significantly influence it. Larger molecules have stronger London dispersion forces, increasing solubility relative to smaller, nonpolar molecules.