A container filled with a sample of an Idea gas at the pressure of 1.5atm. the gas is compressed isothermal ly to one fourth of its original volume. What is the new pressure of the gas?

To find the new pressure of an ideal gas when it is compressed isothermally, we can use Boyle's Law. This law states that for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. In simpler terms, if you decrease the volume of a gas, its pressure increases, provided the temperature remains constant.

Applying Boyle's Law

The formula for Boyle's Law can be expressed as:

P1 × V1 = P2 × V2

Where:

• P1 = initial pressure
• V1 = initial volume
• P2 = final pressure
• V2 = final volume

Given Values

From your question, we have:

• P1 = 1.5 atm
• V2 = V1 / 4 (the gas is compressed to one fourth of its original volume)

Setting Up the Equation

Since we don't know the initial volume (V1), we can express it in terms of V1. Let's substitute V2 into the equation:

1.5 atm × V1 = P2 × (V1 / 4)

Simplifying the Equation

Now, we can simplify this equation. First, multiply both sides by 4 to eliminate the fraction:

4 × 1.5 atm × V1 = P2 × V1

This simplifies to:

6 atm × V1 = P2 × V1

Solving for P2

Next, we can divide both sides by V1 (assuming V1 is not zero):

P2 = 6 atm

Final Result

Therefore, after compressing the gas isothermally to one fourth of its original volume, the new pressure of the gas becomes 6 atm.

This example illustrates how gas behavior can be predicted using fundamental gas laws, which are essential in various fields, including chemistry and engineering. Understanding these principles allows us to manipulate gas conditions effectively in practical applications.