Answer :
Answer:
The final pressure of the gas sample at constant temperature is 1.20 atm.
Explanation:
Boyle's Law : Volume occupied by fixed amount of gas at a given temperature is inversely proportional to pressure .(moles, temperature are constant )
[tex]P\alpha \frac{1}{V}[/tex]
[tex]P = \frac{k}{V}[/tex]
on transposing ,
PV = constant
[tex]P_{1}V_{1} = P_{1}V_{1}[/tex]............(1)
Initial pressure = P1 = 2.00 atm
Final pressure = P2 = ?
Initial volume = V1 = 300.0 mL
Final volume = V2 = 500.0 mL
Putting values of P1 ,V1, V2 in equation (1) and solving for P2
[tex]P_{1}V_{1} = P_{1}V_{1}[/tex]
[tex]2\times 300 = P_{2}\times 500 [/tex]
[tex]P_{2} = \frac{2\times 300 }{500}[/tex]
[tex]P_{2} = 1.2[/tex]
P2 = 1.20 atm at constant temperature
Taking into account the Boyle's law, the final pressure would be 1.2 atm.
Boyle's law
Boyle's law is one of the gas laws that relates the volume and pressure of a certain quantity of gas kept at constant temperature.
This law states that the pressure of a gas in a closed container is inversely proportional to the volume of the container, when the temperature is constant. That is, if the pressure increases, the volume decreases; while if the pressure decreases, the volume increases.
Mathematically, Boyle's law states that the product of pressure and volume is constant:
P×V= k
Studying two different states, an initial state 1 and a final state 2, it is satisfied:
P1× V1= P2×V2
Final pressure in this case
In this case, you know:
- P1= 2 atm
- V1= 300 mL
- P2= ?
- V2= 500 mL
Replacing in Boyle's law:
2 atm× 300 mL= P2×500 mL
Solving:
P2= (2 atm× 300 mL) ÷500 mL
P2= 1.2 atm
Finally, if the volume were increased to 500.00 mL at a constant temperature, the final pressure would be 1.2 atm.
Learn more about Boyle's law:
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