If 0.45 mole of oxygen gas occupies a volume of 1.5 L, what volume will 2.0 moles of oxygen gas occupy at the same temperature and pressure?
The Correct Answer and Explanation is:
To find the volume that 2.0 moles of oxygen gas will occupy at the same temperature and pressure as 0.45 moles occupying 1.5 liters, we can use Avogadro’s Law. Avogadro’s Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas. This relationship can be expressed mathematically as:
[
\frac{V_1}{n_1} = \frac{V_2}{n_2}
]
Where:
- (V_1) is the initial volume (1.5 L),
- (n_1) is the initial number of moles (0.45 moles),
- (V_2) is the final volume (unknown),
- (n_2) is the final number of moles (2.0 moles).
Using this equation, we can rearrange it to solve for (V_2):
[
V_2 = V_1 \times \frac{n_2}{n_1}
]
Now substituting the known values into the equation:
[
V_2 = 1.5 \, \text{L} \times \frac{2.0 \, \text{moles}}{0.45 \, \text{moles}}
]
Calculating this gives:
[
V_2 = 1.5 \, \text{L} \times \frac{2.0}{0.45} \approx 6.67 \, \text{L}
]
Thus, 2.0 moles of oxygen gas will occupy approximately 6.67 liters at the same temperature and pressure.
Explanation:
This calculation demonstrates how gas behavior is consistent with the principles established by Avogadro. According to Avogadro’s Law, gases will expand or contract to fill their container based on the number of moles present. The proportional relationship implies that if the amount of gas doubles, the volume will also double, assuming temperature and pressure remain constant.
In this scenario, we first determined the volume occupied by a known quantity of gas. By setting up a direct ratio based on the number of moles, we calculated the volume for a different quantity. This illustrates the utility of Avogadro’s Law in real-world applications, such as in chemical reactions and gas stoichiometry, where understanding the volume occupied by gases at various amounts can guide predictions and calculations in laboratory settings.