Given:
[tex]P_{1} = \text{3 atm}[/tex]
[tex]T_{1} = \text{300 K}[/tex]
[tex]T_{2} = \text{900 K}[/tex]
Required:
[tex]P_{2}[/tex]
Strategy:
This is a gas law problem. What gas law should we use?
Since the given quantities are pressure and temperature, we will use Gay-Lussac's law. According to this gas law, the pressure of a gas is directly proportional to its absolute temperature keeping the volume and the amount of gas constant.
Caution: The temperature must be converted to kelvin. If the given temperature is in degree Celsius, add 273 or 273.15 to convert it to kelvin.
The formula used for Gay-Lussac's law is
[tex]\boxed{\dfrac{P_{1}}{T_{1}} = \dfrac{P_{2}}{T_{2}}}[/tex]
where:
[tex]P_{1} = \text{initial pressure}[/tex]
[tex]T_{1} = \text{initial temperature}[/tex]
[tex]P_{2} = \text{final pressure}[/tex]
[tex]T_{2} = \text{final temperature}[/tex]
Solution:
Starting with the formula of Gay-Lussac's law
[tex]\dfrac{P_{1}}{T_{1}} = \dfrac{P_{2}}{T_{2}}[/tex]
Multiplying both sides of the equation by T₂ to solve for P₂
[tex]P_{2} = P_{1} \times \dfrac{T_{2}}{T_{1}}[/tex]
Substituting the given values and solving for P₂
[tex]P_{2} = \text{3 atm} \times \dfrac{\text{900 K}}{\text{300 K}}[/tex]
Therefore, the final pressure is
[tex]\boxed{P_{2} = \text{9 atm}}[/tex]
Answer:
P₂ = 9 atm
[tex]\\[/tex]
#BrainlyChallenge2021
