application of pressure law( boyles law)

Question 1

📝 Problem:
A sample of gas occupies a volume of 4.0 liters at a pressure of 2.0 atm. If the volume is decreased to 2.0 liters while keeping the temperature constant, what will be the new pressure?

Answer 1

🧠 Solution:
According to Boyle’s Law, the product of the initial pressure and volume equals the product of the final pressure and volume when the temperature remains constant.

Given:
- Initial pressure (( P_1 )) = 2.0 atm
- Initial volume (( V_1 )) = 4.0 liters
- Final volume (( V_2 )) = 2.0 liters (volume decreased)

We need to find the final pressure (( P_2 )).

Using Boyle’s Law equation:
[ P_1 \times V_1 = P_2 \times V_2

Substitute the given values:
[ 2.0 {atm} \times 4.0 = P_2 \times 2.0 \,

[ 8.0 = 2.0 \times P_2 ]

[ P_2 = \frac{8.0}{2.0} ]

[ P_2 = 4.0 \, {atm} ]

So, the new pressure (( P_2 )) is 4.0 atm.

✨ Answer:
The new pressure of the gas is 4.0 atm.