To find the final pressure of the balloon, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is constant.
Boyle's Law equation:
P₁V₁ = P₂V₂
where: P₁ = initial pressure V₁ = initial volume P₂ = final pressure (to be determined) V₂ = final volume
Given: P₁ = 755 mmHg V₁ = 2.20 L V₂ = 5.16 L
Converting the initial pressure from mmHg to atm:
1 atm = 760 mmHg
P₁ = 755 mmHg / 760 mmHg/atm ≈ 0.9934 atm
Now, we can rearrange the Boyle's Law equation to solve for the final pressure (P₂):
P₂ = (P₁V₁) / V₂
Substituting the given values:
P₂ = (0.9934 atm * 2.20 L) / 5.16 L
P₂ ≈ 0.4258 atm
Therefore, the final pressure of the balloon, when expanded to 5.16 L at constant temperature, is approximately 0.4258 atm.