The volume of a gas is 0.450 L when its pressure is 1.00 atm. If the temperature of the gas does not change, what is the pressure when its volume is changed to 2.00 L? Use [tex]P_1 V_1=P_2 V_2[/tex].
Answer (2)
Using Boyle's Law, the new pressure of the gas when its volume is changed from 0.450 L to 2.00 L is calculated to be 0.225 atm. This is derived from the formula P 1 V 1 = P 2 V 2 . Therefore, P 2 is found to equal 0.225 atm when substituting the given values into the equation.
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We are given the initial volume V 1 = 0.450 L and pressure P 1 = 1.00 atm of a gas.
The volume is changed to V 2 = 2.00 L , and we need to find the new pressure P 2 using Boyle's Law: P 1 V 1 = P 2 V 2 .
Rearrange the formula to solve for P 2 : P 2 = V 2 P 1 V 1 .
Substitute the given values: P 2 = 2.00 L ( 1.00 atm ) ( 0.450 L ) = 0.225 atm . The final answer is 0.225 atm .
Explanation
Understanding the Problem We are given the initial volume and pressure of a gas, and we are asked to find the new pressure when the volume changes, assuming the temperature remains constant. We are also given the formula to use: P 1 V 1 = P 2 V 2 , where P 1 and V 1 are the initial pressure and volume, and P 2 and V 2 are the final pressure and volume.
Listing Given Values We are given: P 1 = 1.00 atm V 1 = 0.450 L V 2 = 2.00 L We need to find P 2 .
Rearranging the Formula Using the formula P 1 V 1 = P 2 V 2 , we can rearrange it to solve for P 2 :
P 2 = V 2 P 1 V 1
Substituting Values and Calculating Now, we substitute the given values into the formula: P 2 = 2.00 L ( 1.00 atm ) ( 0.450 L ) P 2 = 2.00 0.450 atm P 2 = 0.225 atm
Final Answer Therefore, the final pressure of the gas when the volume is changed to 2.00 L is 0.225 atm.
Examples
Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature is kept constant, has many practical applications. For example, in scuba diving, understanding Boyle's Law is crucial for calculating how the volume of air in a diver's lungs changes with depth, as pressure increases underwater. Similarly, in medicine, ventilators use Boyle's Law to control the flow of air into a patient's lungs by adjusting pressure and volume. In everyday life, Boyle's Law is at play in the functioning of engines and refrigeration systems, where gases are compressed and expanded to perform work or transfer heat. Understanding this relationship helps engineers design more efficient and safe systems.
