500 liters of gas in a flexible-walled container are prepared at 700 mmHg and 200°C. The gas is placed into a tank under high pressure. When the tank cools to 20°C, the pressure of the gas is 30 atm. What is the volume of the gas?
Temperatures in Kelvins:
200oC = 273 + 200 = 473 K
20oC = 273 + 20 = 293 K
700 mmHg = "\\frac{700}{760}=0.921\\ atm"
According to the combined gas law,
"\\frac{P_1V_1}{T_1}=\\frac{P_2V_2}{T_2}"
Therefore,
"V_2=\\frac{P_1V_1T_2}{T_1P_2}=\\frac{0.921\\ atm\\times500\\ L\\times293\\ K}{473\\ K\\times30\\ atm}=9.5\\ L"
Answer: 9.5 L
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