A gas occupies 21.0 L at 2.00 atm pressure and 27oC. Calculate its volume at STP.
Use PV = nRT
Remember T must be in kelvin
To calculate the volume of a gas at Standard Temperature and Pressure (STP), you would use the Ideal Gas Law equation: PV = nRT.
Given:
Initial volume (V1) = 21.0 L
Initial pressure (P1) = 2.00 atm
Initial temperature (T1) = 27°C = 27 + 273.15 K
The conditions for STP are:
Standard pressure (P2) = 1 atm
Standard temperature (T2) = 0°C = 0 + 273.15 K
To find the volume at STP, we need to calculate the number of moles of the gas first. Rearranging the Ideal Gas Law equation, we have:
n = (P1 * V1) / (R * T1)
Now, we can calculate the number of moles (n) using the given values and the gas constant R which is 0.0821 L.atm/mol.K:
n = (2.00 atm * 21.0 L) / (0.0821 L.atm/mol.K * (27 + 273.15) K)
After calculating n, we can use the molar volume of a gas at STP, which is 22.4 L/mol, to determine the volume at STP:
V2 = (n * V1) / n2
where n2 is the number of moles at STP:
n2 = (P2 * V2) / (R * T2)
Plugging in the values, we can calculate n2:
n2 = (1 atm * V2) / (0.0821 L.atm/mol.K * 273.15 K)
Finally, we can solve for V2, which is the volume at STP:
V2 = (n * V1 * R * T2) / (P1 * T1)
By substituting the known values, we can find the answer.