Problem 84 - Chemistry: An Atoms-Focused Approach

Question

Nitrous oxide, \(\mathrm{N}_{2} \mathrm{O},\) is used in dental clinics as an anesthetic. The solubility of \(\mathrm{N}_{2} \mathrm{O}\) in water is \(1.1 \mathrm{g} / \mathrm{L}\) at an atmospheric pressure of 1 atm and a temperature of \(20^{\circ} \mathrm{C}\) a. Calculate the Henry's law constant of \(\mathrm{N}_{2} \mathrm{O}\) at \(20^{\circ} \mathrm{C}\). b. Compare the value for \(k_{\mathrm{H}}\) for \(\mathrm{N}_{2} \mathrm{O}\) with the value for \(\mathrm{O}_{2}\) in Table \(11.1 .\) Why are they different?

Step-by-Step Solution

Answer

Question: Calculate the Henry's law constant of Nitrous oxide (N2O) at 20°C and compare it with the value for Oxygen (O2) from a given table. Explain the difference based on the polarity of N2O and O2. Answer: The Henry's law constant for N2O at 20°C is 1.1 g·L⁻¹·atm⁻¹. When compared to the value for O2 from the given table (which is x g·L⁻¹·atm⁻¹, replace x with the actual value), the difference is due to N2O being slightly polar, while O2 is non-polar. This difference in polarity affects their solubility in water and results in different Henry's law constants.

Step 1: Calculate the Henry's law constant of N2O

To calculate the Henry's law constant of N2O, we'll use the Henry's law equation. The solubility (S) is given as 1.1 g/L, and the atmospheric pressure (P) is given as 1 atm. We need to solve the equation for kH: S = kH * P kH = S / P By substituting the given values, we can calculate kH: kH = (1.1 g/L) / (1 atm) kH = 1.1 g·L⁻¹·atm⁻¹ The Henry's law constant of N2O at 20°C is 1.1 g·L⁻¹·atm⁻¹.

Step 2: Compare the values of kH for N2O and O2 and explain the difference

Now, we'll compare the calculated value of kH for N2O with the value for O2 provided in Table 11.1. Let's assume the value of kH for O2 in Table 11.1 is given as x g·L⁻¹·atm⁻¹ (Replace x with the actual value from the table). We need to compare the kH values and discuss why they are different. The differences in kH values are due to the differences in the nature of the gases. N2O is a slightly polar gas, due to its molecular structure whereas O2 is a non-polar gas. This difference in polarity affects their solubility in water and as a result, their Henry's law constants are different. In summary, - Calculate the Henry's law constant of N2O using the provided solubility value kH (N2O) = 1.1 g·L⁻¹·atm⁻¹ - Compare it with the value of kH for O2 provided in Table 11.1 kH (O2) = x g·L⁻¹·atm⁻¹ (Replace x with the actual value from the table) - Explain the difference based on the polarity of N2O and O2

Key Concepts

Solubility

Solubility refers to how much of a gas can dissolve in a liquid at a specific temperature and pressure. When it comes to gases like nitrous oxide (N₂O) dissolving in water, solubility is influenced by factors such as temperature, pressure, and the nature of the gas itself.
Understanding solubility is crucial because it allows us to predict how gases will behave when they are in contact with liquids, like in medical or environmental applications.
For example, nitrogen oxide is moderately soluble in water, and we can calculate its solubility at certain conditions using principles like Henry's Law. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the pressure of that gas above the liquid.

• The equation is:
  \( S = k_H \times P \), where
  - \( S \) is the solubility
  - \( k_H \) is the Henry's Law constant
  - \( P \) is the partial pressure of the gas

By manipulating this equation, we can find out how much gas dissolves in a liquid under various conditions.

Gases in Solution

Gases can dissolve in liquids like water, and this property is essential for various scientific and practical applications. The process is similar to dissolving sugar in tea but involves molecules of a gas instead.
In solutions, gas molecules occupy spaces between the liquid molecules, forming an even distribution. This distribution is influenced by factors including temperature and pressure.
- **Temperature:** Typically, gases are less soluble in water as the temperature increases. This happens because higher temperatures give gas molecules more energy to escape from the liquid. - **Pressure:** According to Henry's Law, an increase in pressure typically increases gas solubility. When gas molecules are pressed into the liquid surface, more of them are absorbed by the liquid. A practical example is how carbon dioxide bubbles form in a soda bottle when it's opened. The pressure inside the bottle keeps CO₂ dissolved, but once opened, the pressure drops, and the gas escapes, forming bubbles. Understanding how gases dissolve is crucial for comprehending phenomena like the fizz in drinks or how our bodies absorb oxygen from the air we breathe.

Polarity and Solubility

Polarity plays a significant role in the solubility of substances. Polarity arises from the unequal sharing of electrons in a molecule, leading to a distribution of electrical charge. Nitrous oxide (N₂O) is slightly polar due to its molecular structure, which affects how it interacts with water molecules. On the other hand, oxygen (O₂) is non-polar, exhibiting different solubility characteristics.

- **Polar Molecules:**

• These have partial positive and negative charges within the molecule.
• Water is a polar solvent, which means it can dissolve other polar substances more readily than non-polar ones.

- **Non-polar Molecules:**

• O₂, being non-polar, does not interact as strongly with the polar water molecules as polar gases do.
• This leads to a lower solubility of non-polar gases compared to polar ones in water.

In essence, understanding the polarity helps explain why some gases dissolve more readily in water than others. For instance, the Henry's Law constant reflects this difference as it varies between N₂O and O₂ due to their varying polarities.