A balloon containing methane gas has a volume of 1.03 L at 99.0 °C . What volume will the balloon occupy at 198 °C ?
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Question:
A balloon containing methane gas has a volume of 1.03 L at 99.0 °C . What volume will the balloon occupy at 198 °C ?
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Answer:The balloon will occupy a volume of 1.32L. Explanation:Given the following data;Original Volume, V1 = 1.03LOriginal Temperature, T1 = 99°CNew Temperature, T2 = 198°CTo find new volume V2, we would use Charles' law. Charles states that when the pressure of an ideal gas is kept constant, the volume of the gas is directly proportional to the absolute temperature of the gas. Mathematically, Charles is given by;[tex] VT = K[/tex] [tex] \frac{V1}{T1} = \frac{V2}{T2}[/tex] Converting T1, from Celsius to Kelvin = 273 + 99 = 372KConverting, T2, from Celsius to Kelvin = 273 + 198 = 471K[tex] \frac{V1}{T1} = \frac{V2}{T2}[/tex] Making V2 as the subject formula, we have;[tex] V_{2}= \frac{V1}{T1} * T_{2}[/tex] [tex] V_{2}= \frac{1.03}{372} * 471[/tex][tex] V_{2}= 0.0028 * 471[/tex]V2 = 1.32LTherefore, the balloon will occupy a volume of 1.32L at 198°C
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