A 3.0 L container holds a sample of oxygen gas at 1.5 atm pressure. If the pressure increases to 2.0 atm and the temperature remain constant, what is the new volume of the container?
volume is inversely proportional to temperature
3.0 L * 1.5 atm = x L * 2.0 atm
To solve this problem, we can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant.
Boyle's Law equation: P1V1 = P2V2
Where:
P1 = Initial pressure
V1 = Initial volume
P2 = Final pressure
V2 = Final volume
Given:
P1 = 1.5 atm
V1 = 3.0 L
P2 = 2.0 atm
Plugging in the given values into Boyle's Law equation:
1.5 atm * 3.0 L = 2.0 atm * V2
Simplifying the equation:
4.5 L = 2.0 atm * V2
To find V2, divide both sides of the equation by 2.0 atm:
V2 = 4.5 L / 2.0 atm
V2 = 2.25 L
Therefore, the new volume of the container is 2.25 L.
To find the new volume of the container, 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 can be mathematically expressed as:
P₁V₁ = P₂V₂
In this case, we have:
P₁ = 1.5 atm (initial pressure)
V₁ = 3.0 L (initial volume)
P₂ = 2.0 atm (final pressure)
V₂ = ? (final volume)
We can rearrange Boyle's Law to solve for V₂:
V₂ = (P₁V₁) / P₂
Substituting the given values into the formula:
V₂ = (1.5 atm * 3.0 L) / 2.0 atm
Calculating:
V₂ = 4.5 L / 2.0
V₂ = 2.25 L
Therefore, the new volume of the container is 2.25 L when the pressure increases to 2.0 atm and the temperature remains constant.