A sample of gaseous O2, occupies a volume of 4.5 L at a pressure of 0.871 atm at 25°C. What volume, in liters, will this gas occupy if the pressure is decreased to 0.639 atm?
The correct answer and explanation is:
To solve this problem, we can use Boyle’s Law, which states that for a given amount of gas at constant temperature, the pressure and volume of the gas are inversely proportional. This means that when the pressure of a gas decreases, its volume increases, and vice versa, provided the temperature remains unchanged.
The formula for Boyle’s Law is: P1V1=P2V2P_1 V_1 = P_2 V_2
Where:
- P1P_1 is the initial pressure
- V1V_1 is the initial volume
- P2P_2 is the final pressure
- V2V_2 is the final volume (the value we need to find)
Given:
- P1=0.871 atmP_1 = 0.871 \, \text{atm}
- V1=4.5 LV_1 = 4.5 \, \text{L}
- P2=0.639 atmP_2 = 0.639 \, \text{atm}
Step 1: Rearranging Boyle’s Law to solve for V2V_2
V2=P1V1P2V_2 = \frac{P_1 V_1}{P_2}
Step 2: Substituting the known values:
V2=(0.871 atm)×(4.5 L)0.639 atmV_2 = \frac{(0.871 \, \text{atm}) \times (4.5 \, \text{L})}{0.639 \, \text{atm}} V2=3.9195 L\cdotpatm0.639 atmV_2 = \frac{3.9195 \, \text{L·atm}}{0.639 \, \text{atm}}
Step 3: Calculating the final volume:
V2≈6.13 LV_2 \approx 6.13 \, \text{L}
Thus, the final volume of the gas will be approximately 6.13 L when the pressure decreases to 0.639 atm.
Explanation:
The relationship between pressure and volume in a gas is inversely proportional, meaning that when the pressure decreases, the volume increases. This result demonstrates that as the gas’s pressure is reduced from 0.871 atm to 0.639 atm, the volume expands. This behavior is consistent with the ideal gas law, which assumes that gases behave ideally under most conditions, particularly when the temperature is held constant.
Since the temperature (25°C) is assumed to be constant and the gas is not changing in composition, Boyle’s Law is the appropriate method for solving this problem.