The conditions of standard temperature and pressure STP are a temperature of 0.00 ∘C and a pressure of 1.00 atm.
Part A
How many liters does 2.60 mol of any ideal gas occupy at STP?
answer: V=_____L
Part B
For a scientist on Venus, an absolute pressure of 1 Venusian-atmosphere is 92 Earth-atmospheres. Of course she would use the Venusian-atmosphere to define STP. Assuming she kept the same temperature, how many liters would 4.60 mol of ideal gas occupy on Venus?
answer: V=_ L
The Correct Answer and Explanation is :
Part A:
To find the volume occupied by 2.60 moles of any ideal gas at STP, we use the ideal gas law ( PV = nRT ), where:
- ( P ) is the pressure,
- ( V ) is the volume,
- ( n ) is the number of moles of gas,
- ( R ) is the ideal gas constant,
- ( T ) is the temperature.
At STP, the temperature (T) is 0°C, which converts to 273.15 K, and the pressure (P) is 1.00 atm. The ideal gas constant (R) is generally ( 0.0821 \, L \cdot atm/(mol \cdot K) ).
Plugging these values into the ideal gas law rearranged for volume ( V ), we get:
[
V = \frac{nRT}{P}
]
Substituting in the values:
[
V = \frac{2.60 \, mol \times 0.0821 \, L \cdot atm/(mol \cdot K) \times 273.15 \, K}{1.00 \, atm}
]
[
V = 58.4 \, L
]
Thus, ( 2.60 \, mol ) of any ideal gas occupies ( 58.4 \, liters ) at STP.
Part B:
For the scientist on Venus, the pressure is defined as 1 Venusian-atmosphere, which is equivalent to 92 Earth-atmospheres. The temperature remains the same (273.15 K), and the amount of gas is 4.60 moles. Again using the ideal gas law ( V = \frac{nRT}{P} ), we substitute the new conditions:
[
V = \frac{4.60 \, mol \times 0.0821 \, L \cdot atm/(mol \cdot K) \times 273.15 \, K}{92 \, atm}
]
[
V = 0.637 \, L
]
Thus, ( 4.60 \, mol ) of ideal gas occupies approximately ( 0.637 \, liters ) under the conditions defined as STP on Venus.
This calculation shows how significantly the conditions on Venus affect the volume of gas. At a much higher pressure, the same amount of gas occupies a much smaller volume compared to Earth’s STP. This illustrates the inverse relationship between pressure and volume (Boyle’s Law) in the ideal gas law, highlighting how extreme conditions, such as those on Venus, can lead to dramatically different physical properties.