A balloon at contains 0.5 L of gas at a constant pressure of 1.0 atm. If the pressure is increased to 3.0 atm, what will be the volume of the gas?
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. Boyle's Law is mathematically represented as:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume of the gas, and P₂ and V₂ are the final pressure and volume of the gas.
Let's substitute the given values into the equation:
P₁ = 1.0 atm
V₁ = 0.5 L
P₂ = 3.0 atm
V₂ = ?
Using the equation P₁V₁ = P₂V₂:
(1.0 atm)(0.5 L) = (3.0 atm)(V₂)
Solving for V₂:
0.5 L = (3.0 atm)(V₂)
V₂ = 0.5 L / (3.0 atm)
V₂ = 0.1667 L
Therefore, when the pressure is increased from 1.0 atm to 3.0 atm, the volume of the gas will be approximately 0.1667 L.