Textbook Question
Many gases are shipped in high-pressure containers. Consider a steel tank whose volume is 210.0 L that contains O2 gas at a pressure of 16,500 kPa at 23 °C. (a) What mass of O2 does the tank contain?
7. Gases
The Ideal Gas Law
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A container with a movable piston contains 2.0 moles of argon gas. When the volume of the container is 1.5 L, the pressure is 2.4 atm. Calculate the pressure of the container when the piston is raised to give a volume of 2.5 L. Assume the temperature remains constant.
A
1.4 atm
B
1.6 atm
C
2.8 atm
D
3.2 atm
E
4.0 atm
Verified step by step guidance1
Identify the problem as an application of Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. This can be expressed as \( P_1 V_1 = P_2 V_2 \).
Assign the known values to the variables in Boyle's Law: \( P_1 = 2.4 \) atm, \( V_1 = 1.5 \) L, and \( V_2 = 2.5 \) L. The goal is to find \( P_2 \), the pressure when the volume is 2.5 L.
Rearrange the equation \( P_1 V_1 = P_2 V_2 \) to solve for \( P_2 \). This gives \( P_2 = \frac{P_1 V_1}{V_2} \).
Substitute the known values into the rearranged equation: \( P_2 = \frac{2.4 \text{ atm} \times 1.5 \text{ L}}{2.5 \text{ L}} \).
Perform the calculation to find \( P_2 \). This will give you the pressure of the container when the volume is increased to 2.5 L.
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