An ideal gas in a sealed container has an initial volume of 2.55 L. At constant pressure, it cools to 16.00 degrees Celsius, resulting in a final volume of 1.75 L. What was the initial temperature?
Answer (3)
Use ideal gas law PV=nRT. The pressure, number of moles, and gas constant are unchanged. Rearrange ideal gas law to get n= PV1/RT1= PV2/RT2 now you can cancel out P and R to get V1/T1 = V2/T2 you know V1= 2.55 L, V2= 1.75 L, T2= 16 degC, you can solve for T1( the initial temperature).
To determine the initial temperature of an ideal gas in a sealed container when given the final temperature, final volume, and assuming constant pressure, we can use Charles's Law. Charles's Law states that at constant pressure, the volume of an ideal gas is directly proportional to its temperature in Kelvins. The formula derived from this law is V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature.
First, convert the final temperature from degrees Celsius to Kelvin. T2 = 16.00 °C + 273.15 = 289.15 K.
Second, apply Charles's Law. V1/T1 = V2/T2, where V1 = 2.55 L and V2 = 1.75 L.
Now solve for T1 (initial temperature in Kelvins): T1 = (V1 × T2) / V2 T1 = (2.55 L × 289.15 K) / 1.75 L
Calculate T1: T1 = 422.6375 K
Finally, convert T1 back to Celsius if needed: T1 °C = 422.6375 K - 273.15 = 149.4875 °C
Therefore, the initial temperature of the gas was approximately 149.49 °C.
The initial temperature of the gas was calculated to be approximately 148.14 °C using Charles's Law. This law states that the volume of an ideal gas is directly proportional to its temperature at constant pressure. Proper conversions and rearranging of the formula provide the final result.
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