application of pressure law ( general gas law )

Question 1

📝 Problem:
A sample of gas has an initial pressure of 2.0 atm, volume of 3.0 liters, and temperature of 300 K. If the volume of the gas is increased to 4.0 liters while keeping the temperature constant, what will be the new pressure of the gas?

Answer 1

🧠 Solution:
We can use the general gas law equation:
[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} ]

Given:
- Initial pressure (( P_1 )) = 2.0 atm
- Initial volume (( V_1 )) = 3.0 liters
- Initial temperature (( T_1 )) = 300 K
- Final volume (( V_2 )) = 4.0 liters (volume increased)
- Temperature remains constant, so ( T_2 = T_1 )

Substitute the given values:
[ \frac{2.0 \, \text{atm} \times 3.0 \, \text{L}}{300 \, \text{K}} = \frac{P_2 \times 4.0 \, \text{L}}{300 \, \text{K}} ]

Simplify:
[ \frac{6.0}{300} = \frac{P_2 \times 4.0}{300} ]

[ \frac{P_2 \times 4.0}{300} = \frac{6.0}{300} ]

[ P_2 \times 4.0 = 6.0 ]

[ P_2 = \frac{6.0}{4.0} ]

[ P_2 = 1.5 \, \text{atm} ]

So, the new pressure of the gas (( P_2 )) is 1.5 atm.