A container with a volume of 2.0 L is filled with a gas at a pressure of 1.5 atm. By decreasing the volume of the container to 1.0 L, what is the resulting pressure? Type in your answer using the correct number of significant figures. Remember to use the formula for Boyle's law: [tex]$P_1 V_1=P_2 V_2$[/tex]
Answer (2)
State Boyle's Law: P 1 V 1 = P 2 V 2 .
Rearrange the formula to solve for the final pressure: P 2 = V 2 P 1 V 1 .
Substitute the given values: P 2 = 1.0 L ( 1.5 atm ) ( 2.0 L ) .
Calculate the final pressure: P 2 = 3.0 atm .
Explanation
Problem Analysis and Given Data We are given the initial volume V 1 = 2.0 L and initial pressure P 1 = 1.5 atm of a gas. The volume is decreased to V 2 = 1.0 L, and we need to find the resulting pressure P 2 . We will use Boyle's Law, which states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional: P 1 V 1 = P 2 V 2 .
Solving for the Final Pressure To find the final pressure P 2 , we can rearrange Boyle's Law to solve for P 2 : P 2 = V 2 P 1 V 1
Substituting the Values Now, we substitute the given values into the equation: P 2 = 1.0 L ( 1.5 atm ) ( 2.0 L )
Calculating the Result Calculating the final pressure: P 2 = 1.0 L 3.0 atm L = 3.0 atm Since the given values have two significant figures, the final answer should also have two significant figures.
Final Answer The resulting pressure is 3.0 atm.
Examples
Boyle's Law is useful in scenarios like scuba diving, where understanding the relationship between pressure and volume is crucial for managing air supply. As a diver descends, the pressure increases, and the volume of air in their lungs decreases. Similarly, in weather forecasting, Boyle's Law helps predict changes in atmospheric pressure and volume, which are essential for understanding weather patterns. In the medical field, ventilators use Boyle's Law to control the volume and pressure of air delivered to patients, ensuring proper respiratory support.
By applying Boyle's Law, we can determine that the final pressure, after decreasing the volume from 2.0 L to 1.0 L while starting with a pressure of 1.5 atm, is 3.0 atm.
;
