A gas has a pressure of 2.96 atm when its
volume is 3.93 L. What will the pressure
be when the volume is changed to 1.09 L,
assuming constant temperature? Express the
final pressure in torr.
Answer in units of torr
P1=2.96
P2=?
V1=3.93L
V2=1.09L
**** 1 atm = 760 torr
Use P1V1/T1=P2V2/T2 and solve for P2. Assuming T1=T2, you can ignore the T's and rewrite the equation as P1V1=P2V2.
Rearranging the equation results in (P1V1)/P2=V2
Plug in your values and solve for V2
Afterwards multiply by the conversion provided to get your answer in torr.
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. The formula for Boyle's Law is:
P₁V₁ = P₂V₂
Where:
P₁ = initial pressure (2.96 atm)
V₁ = initial volume (3.93 L)
P₂ = final pressure (what we need to find)
V₂ = final volume (1.09 L)
To solve for P₂, we can rearrange the equation:
P₂ = (P₁V₁) / V₂
Substituting the given values:
P₂ = (2.96 atm * 3.93 L) / 1.09 L
P₂ = 10.6728 atm
Now, to express the final pressure in torr, we need to convert atm to torr.
1 atm = 760 torr
Converting the final pressure:
P₂ = 10.6728 atm * 760 torr/atm
P₂ ≈ 8113.65 torr
Therefore, the final pressure, assuming constant temperature, would be approximately 8113.65 torr.