A sample of oxygen occupies 1.00 L. If the temperature remains constant and the pressure on oxygen is decreased to one-third the orginal pressure, what is the new volume?
3.00L
P1V1 = P2V2
To solve this problem, we can use the combined gas law, which states that:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure
V2 = Final volume
T2 = Final temperature
Given:
Initial volume, V1 = 1.00 L
Initial pressure, P1 = ?
Final pressure, P2 = 1/3 * P1
Final volume, V2 = ?
Since the temperature remains constant, we can cancel out T1 and T2 from the equation.
Now, let's substitute the given values into the equation:
(P1 * 1.00 L) / T1 = ((1/3 * P1) * V2) / T2
Since T1 and T2 are constant, we can remove them from the equation:
P1 * 1.00 L = (1/3 * P1) * V2
Now, let's simplify the equation:
1.00 L = (1/3 * P1 / P1) * V2
1.00 L = (1/3) * V2
To find the value of V2, we can multiply both sides of the equation by 3:
3 * 1.00 L = V2
Therefore, the new volume, V2, is 3.00 L.
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 can be mathematically expressed as:
P₁V₁ = P₂V₂
Where:
P₁ and V₁ are the initial pressure and volume
P₂ and V₂ are the final pressure and volume
In this case, the initial volume (V₁) is given as 1.00 L, and the final pressure (P₂) is one-third of the initial pressure (P₁).
Let's substitute these values into the equation and solve for the final volume (V₂):
P₁V₁ = P₂V₂
We can rewrite the equation as:
V₂ = (P₁V₁) / P₂
Given that P₂ = P₁ / 3, we can substitute this value:
V₂ = (P₁V₁) / (P₁ / 3)
Simplifying further:
V₂ = (P₁V₁) * (3 / P₁)
The P₁ term cancels out:
V₂ = V₁ * 3
Now, substitute the initial volume value:
V₂ = 1.00 L * 3
Calculating the result:
V₂ = 3.00 L
Therefore, the new volume of oxygen when the pressure is decreased to one-third of the original pressure is 3.00 L.