Problem 89 - Chemistry Matter and Change

Question

At a pressure of 1.5 atm, the solubility of a gas is 0.54 \(\mathrm{g} / \mathrm{L}\) . Calculate the solubility when the pressure is doubled.

Step-by-Step Solution

Answer

The solubility at 3 atm is 1.08 g/L.

Step 1: Understand the Relationship

The solubility of a gas in a liquid is proportional to the pressure of the gas above the liquid. This relationship is described by Henry's Law.

Step 2: Apply Henry's Law Formula

Henry's Law states that \( S_1/P_1 = S_2/P_2 \), where \( S_1 \) is the initial solubility of the gas, \( P_1 \) is the initial pressure, \( S_2 \) is the solubility at the new pressure, and \( P_2 \) is the new pressure.

Step 3: Identify Given Values

We have \( S_1 = 0.54 \), \( P_1 = 1.5 \) atm, and \( P_2 = 2 \times 1.5 \) atm = 3 atm. We need to find \( S_2 \).

Step 4: Solve for New Solubility

Re-arrange the equation to solve for \( S_2 \): \( S_2 = S_1 \times \frac{P_2}{P_1} \). Substitute the known values to get \( S_2 = 0.54 \times \frac{3}{1.5} \).

Step 5: Calculate the Result

Calculate \( S_2 \): \( 0.54 \times \frac{3}{1.5} = 0.54 \times 2 = 1.08 \). Thus, the solubility of the gas at 3 atm pressure is 1.08 g/L.

Key Concepts

gas solubility

Gas solubility refers to the amount of a gas that can dissolve in a liquid at a specific temperature and pressure. It's an important concept, especially in solutions where gases like oxygen, carbon dioxide, or nitrogen dissolve in water or other solvents. Solubility indicates how readily a gas will dissolve and reach a balance between the gas phase and the dissolved phase in the liquid.
Factors like temperature and pressure play a crucial role in determining the solubility of a gas. Generally, gases are less soluble in warmer liquids and more soluble under higher pressure conditions.

pressure and solubility relationship

The relationship between pressure and gas solubility is well-defined by Henry's Law. This principle states that the solubility of a gas in a liquid is directly proportional to the pressure of the gas over the liquid. Practically, this means that increasing the pressure will increase the rate at which a gas dissolves in a liquid.
For example, when you double the pressure, the solubility of the gas also doubles, given the temperature remains constant.

• Higher pressure increases solubility.
• Lower pressure decreases solubility.

Understanding this interaction is essential for calculating how factors like pressure impact gas dissolution in solutions used across various scientific fields.

solubility calculation

Calculating solubility involves using Henry's Law, where the formula is expressed as \( S_1/P_1 = S_2/P_2 \). This equation helps you compute the change in solubility when pressure conditions change. In this exercise, we start by identifying known variables: the initial solubility \( S_1 \), initial pressure \( P_1 \), and the new pressure \( P_2 \).
Next, rearrange the formula to solve for \( S_2 \), the solubility at the new pressure: \[ S_2 = S_1 \times \frac{P_2}{P_1} \]By substituting the given values, you can accurately calculate the new solubility under different pressure conditions. Here, with different pressures, having these calculations correct means precise predictions of how much gas can dissolve under real-world conditions.

chemistry problem solving

Solving chemistry problems efficiently requires an understanding of the fundamental principles, like Henry's Law for gas solubility. Begin by identifying the core concepts involved in the problem, such as pressure affects in a gas-liquid solution.
Next, apply these concepts logically, making sure to understand the relationships and equations that tie these principles together, such as setting up the relevant formulae correctly.

• Identify what you know: the variables and relationships.
• Set up the right equations using these variables.
• Perform calculations carefully, using precise unit conversion if needed.

By accurately applying these steps, you build effective problem-solving skills that are invaluable in tackling various scientific questions and experiments.