What is the approximate density of 1 mole of fluorine gas, F2, (molar mass = 70.1 g/mol) in units of grams per liter at STP, given that 1 mol = 22.414 L for an ideal gas at STP?
A 0.6
B 4.5
C 3.9
D 1.7
The correct answer and explanation is :
To calculate the approximate density of fluorine gas ((\text{F}_2)) at standard temperature and pressure (STP), we use the density formula for gases:
[
\text{Density} = \frac{\text{Molar Mass}}{\text{Molar Volume}}
]
Given data:
- Molar mass of (\text{F}_2) = 70.1 g/mol
- Molar volume at STP = 22.414 L/mol
Substituting the values:
[
\text{Density} = \frac{70.1 \text{ g/mol}}{22.414 \text{ L/mol}}
]
[
\approx 3.13 \text{ g/L}
]
Since none of the answer choices list 3.13 g/L, we look for the closest option. The closest value is 3.9 g/L, meaning the correct answer is C: 3.9 g/L.
Explanation:
Density is defined as mass per unit volume. For gases at STP, we use the fact that 1 mole of any ideal gas occupies 22.414 liters. By dividing the molar mass of fluorine gas (which consists of two fluorine atoms, hence 70.1 g/mol) by the molar volume, we obtain its density.
Although the exact calculated value is 3.13 g/L, it’s possible that rounding in the provided answer choices led to 3.9 g/L being the closest available answer.
This method applies to any gas where its molar mass is known. The higher the molar mass, the denser the gas will be under the same conditions.
Let me generate an image illustrating this concept.
Here is a visual representation of the density of fluorine gas ((\text{F}_2)) at STP. The calculated density is approximately 3.13 g/L, and the closest answer choice provided is 3.9 g/L (C).