A sample of oxygen at room temperature occupies a volume of 5.00x102 mL at 1.50 atm pressure. What pressure (in atm) must be applied to compress the gas to a volume of only 1.50x102 mL? Assume the temperature is constant.
P1V1 = P2V2
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To solve this problem, we can use Boyle's Law which states that the volume of a given amount of gas is inversely proportional to the pressure when temperature is constant.
Boyle's Law can be stated as P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
Given:
Initial volume (V₁) = 5.00x10² mL
Initial pressure (P₁) = 1.50 atm
Final volume (V₂) = 1.50x10² mL
We need to find the final pressure (P₂).
Using Boyle's Law, we can set up the equation as follows:
P₁V₁ = P₂V₂
Substituting the given values:
(1.50 atm)(5.00x10² mL) = P₂(1.50x10² mL)
Simplifying the equation:
750x10² atm mL = 1.50x10² P₂ mL
Dividing both sides by 1.50x10² mL:
P₂ = (750x10² atm mL) / (1.50x10² mL)
Canceling out the mL units:
P₂ = 750/1.50 atm
Calculating:
P₂ = 500 atm
Therefore, the pressure required to compress the gas to a volume of 1.50x10² mL is 500 atm.
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 can be mathematically expressed as:
P1 * V1 = P2 * V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
Initial volume (V1) = 5.00x102 mL
Initial pressure (P1) = 1.50 atm
Final volume (V2) = 1.50x102 mL
We need to find the final pressure (P2).
Using the formula for Boyle's Law, we can rearrange the equation to solve for P2:
P2 = (P1 * V1) / V2
Substituting the given values, we get:
P2 = (1.50 atm * 5.00x102 mL) / (1.50x102 mL)
Simplifying the expression, we find:
P2 = (1.50 * 5.00) atm
P2 = 7.50 atm
Therefore, a pressure of 7.50 atm must be applied to compress the gas to a volume of 1.50x102 mL, assuming the temperature remains constant.