A Sample of Carbon Dioxide and Boyle's Law
Calculating Pressure Using Boyle's Law
A sample of carbon dioxide occupies a volume of 3.50 L at 125 kPa. What pressure would the gas exert if the volume was decreased to 2.00 L but the temperature was held constant?
Final answer:
Using Boyle's Law, the new pressure of a sample of carbon dioxide when its volume is decreased to 2.00 L at constant temperature is calculated to be 218.75 kPa.
Explanation:
The question involves the use of the Boyle's Law, which states that for a fixed amount of gas at a constant temperature, the volume of a gas is inversely proportional to the pressure it exerts. To calculate the new pressure when the volume decreases, we use the formula:
P1 × V1 = P2 × V2
Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume. Plugging in the values:
125 kPa × 3.50 L = P2 × 2.00 L
To find P2:
P2 = (125 kPa × 3.50 L) / 2.00 L
P2 = 218.75 kPa
So, the pressure the gas would exert if the volume was decreased to 2.00 L while keeping temperature constant would be 218.75 kPa.
What is Boyle's Law and how is it used to calculate pressure changes in gases? Boyle's Law is a fundamental principle in gas physics that describes the inverse relationship between the pressure and volume of a gas at constant temperature. It states that as the volume of a gas decreases, the pressure it exerts increases, and vice versa. The law can be expressed mathematically 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, respectively. By rearranging the formula, one can calculate the new pressure of a gas when its volume is changed while keeping the temperature constant, as shown in the example above.