A sample of gas occupies a volume of 7.50 L at 0.988 atm and 301 K. At what temperature is the volume of the gas 4.00 L if the pressure is kept constant.
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To solve for the new temperature (T2) when the volume of the gas changes while keeping the pressure constant, we can use Charles's Law, which states that for a given mass of an ideal gas at constant pressure, the volume is directly proportional to the absolute temperature (in Kelvin). Charles's Law can be mathematically represented as:
V1/T1 = V2/T2
Where, V1 = initial volume = 7.50 L T1 = initial temperature = 301 K V2 = final volume = 4.00 L T2 = final temperature = ?
Since the pressure remains constant, we can rearrange the formula to solve for T2:
T2 = (V2 * T1) / V1
Now we can plug the known values into the equation to find T2:
T2 = (4.00 L * 301 K) / 7.50 L
T2 = 1204 / 7.50
T2 ≈ 160.53 K
Thus, the temperature at which the volume of the gas is 4.00 L with the pressure kept constant is approximately 160.53 Kelvin