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? $$ \begin{array}{lc} \hline \text { Gas } & \text { Solubility (mM) } \\ \hline \mathrm{CH}_{4} \text { (methane) } & 1.3 \\ \mathrm{C}_{2} \mathrm{H}_{6} \text { (ethane) } & 1.8 \\ \mathrm{C}_{2} \mathrm{H}_{4} \text { (ethylene) } & 4.7 \\ \mathrm{~N}_{2} & 0.6 \\ \mathrm{O}_{2} & 1.2 \\ \mathrm{NO} & 1.9 \\ \mathrm{H}_{2} \mathrm{~S} & 99 \\ \mathrm{SO}_{2} & 1476 \\ \hline \end{array} $$

Step by step solution

01

(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.

02

(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.

03

(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.

04

(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.

05

(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.

06

(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.

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