How many liters of gas are found in 0.15 moles of chlorine gas?
The correct answer and explanation is:
Correct Answer:
At standard temperature and pressure (STP), 0.15 moles of chlorine gas (Cl₂) occupy approximately 3.36 liters.
Explanation (Approx. 300 Words):
To determine how many liters of chlorine gas are present in 0.15 moles, we use the concept of molar volume of a gas at standard temperature and pressure (STP).
STP is defined as:
- Temperature = 0°C or 273.15 K
- Pressure = 1 atm
At STP, 1 mole of any ideal gas occupies 22.4 liters.
Step-by-Step Calculation:
We are given:
- Moles of chlorine gas (Cl₂) = 0.15 mol
- Molar volume at STP = 22.4 L/mol
Use the formula: Volume (L)=Moles×Molar Volume\text{Volume (L)} = \text{Moles} \times \text{Molar Volume} Volume=0.15 mol×22.4 L/mol=3.36 L\text{Volume} = 0.15 \, \text{mol} \times 22.4 \, \text{L/mol} = 3.36 \, \text{L}
So, 0.15 moles of Cl₂ gas occupy 3.36 liters at STP.
Why This Works:
Chlorine gas (Cl₂) behaves like an ideal gas under standard conditions. The ideal gas law relates pressure, volume, temperature, and amount of gas. At STP, the molar volume simplifies calculations: PV=nRT⇒V=nRTPPV = nRT \Rightarrow V = \frac{nRT}{P}
Where:
- VV = Volume
- nn = Moles
- RR = Ideal gas constant
- TT = Temperature (in Kelvin)
- PP = Pressure
At STP, these values are constant, leading to the standardized 22.4 L per mole.
This method is widely used in chemistry for quick estimations involving gases when conditions are known to be STP. If the temperature or pressure differs from STP, the ideal gas law must be used with actual values.