Final answer:
To calculate the volume of a gas at STP from an initial volume of 2.000L at a pressure of 740kPa, use the combined gas law, rearranging it to solve for the new volume once the gas is brought to STP conditions (0°C, 101.325 kPa). The volume can be found using the formula V2 = (P1 × V1) / P2.
Step-by-step explanation:
Finding the Volume of Gas at STP
To calculate the volume of a gas at standard temperature and pressure (STP), we can use the combined gas law. In this case, we want to find out what the new volume would be if a gas with an initial volume of 2.000L and an initial pressure of 740kPa is brought to STP.
STP is defined as a temperature of 0°C or 273.15K and a pressure of 1 atmosphere (atm), which is equivalent to 101.325kPa. We use the combined gas law, which states that the product of pressure and volume divided by temperature (PV/T) remains constant if the amount of gas is unchanged (assuming ideal behavior). Therefore:
(P1V1)/T1 = (P2V2)/T2
Since we're only given the initial conditions and the question specifies that the final conditions are at STP, we have:
- Initial Pressure (P1) = 740 kPa
- Initial Volume (V1) = 2.000 L
- Initial Temperature (T1) — Not provided; could be assumed as room temperature in some questions but is irrelevant here as we are focused on pressure-volume changes at constant temperature
- Final Pressure (P2) = 101.325 kPa
- Final Volume (V2) = ?
- Final Temperature (T2) — Again, not needed in this case.
Rearranging and solving for the final volume (V2), we get:
V2 = (P1 × V1) / P2
Plugging in the known values, we can find the new volume at STP:
V2 = (740 kPa × 2.000 L) / 101.325 kPa
Now just calculate V2 to get the volume of the gas at STP.