Answer:
the original volume of the gas is approximately 1302.86 mL. ️
Explanation:
Given that the gas undergoes a change in pressure while maintaining constant temperature and mass, we can use the ideal gas law to find the original volume. The ideal gas law states:
[ PV = nRT ]
Where:
(P) is the pressure (initial or final)
(V) is the volume (initial or final)
(n) is the number of moles of gas (which remains constant)
(R) is the ideal gas constant
(T) is the absolute temperature (which remains constant)
Since the temperature and mass are constant, we can use the relationship:
[ P_1V_1 = P_2V_2 ]
where:
(P_1) is the initial pressure (350 torr)
(V_1) is the initial volume (which we need to find)
(P_2) is the final pressure (1.2 atm)
(V_2) is the final volume (500 mL, converted to liters)
Let’s calculate the original volume of the gas:
Convert the final volume to liters: [ V_2 = 500 , \text{mL} = 0.5 , \text{L} ]
Convert the initial pressure from torr to atm: [ P_1 = \frac{350}{760} , \text{atm} ]
Use the relationship: [ P_1V_1 = P_2V_2 ] [ V_1 = \frac{P_2V_2}{P_1} ] Substituting the given values: [ V_1 = \frac{(1.2 , \text{atm}) \cdot (0.5 , \text{L})}{\frac{350}{760} , \text{atm}} ]
Calculate the original volume: [ V_1 \approx 1302.86 , \text{mL} ]
