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Multiple Choice
The system volume is 10 L at STP. If the temperature decreases to 30 K, what is the new volume, assuming pressure remains constant?
A
5.00 L
B
3.00 L
C
10.00 L
D
1.34 L
Verified step by step guidance
1
Start by understanding the relationship between temperature and volume at constant pressure, which is described by Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant.
Express Charles's Law mathematically: \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \), where \( V_1 \) and \( T_1 \) are the initial volume and temperature, and \( V_2 \) and \( T_2 \) are the final volume and temperature.
Identify the known values: \( V_1 = 10 \text{ L} \), \( T_1 = 273 \text{ K} \) (since STP is 273 K), and \( T_2 = 30 \text{ K} \). You need to find \( V_2 \).
Rearrange the equation to solve for \( V_2 \): \( V_2 = V_1 \times \frac{T_2}{T_1} \). Substitute the known values into the equation.
Calculate \( V_2 \) using the substituted values: \( V_2 = 10 \text{ L} \times \frac{30 \text{ K}}{273 \text{ K}} \). This will give you the new volume of the gas at 30 K.