A balloon originally had a volume of 6.63 L at 86 °C and a pressure of 684 torr. The balloon must be cooled to __________°C to reduce its volume to 6.03 L (at constant pressure). Express answer to the tenth decimal place
P1/T1 = P2/T2. Don't forget to use T in Kelvin. After find T, convert from Kelvin to celsius.
To find the temperature at which the balloon must be cooled to reduce its volume to 6.03 L, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant.
Charles's Law can be represented using the formula:
V1/T1 = V2/T2
Where:
V1 = initial volume = 6.63 L
T1 = initial temperature = 86 °C (convert to Kelvin by adding 273.15) = 359.15 K
V2 = final volume = 6.03 L
T2 = final temperature (to be determined)
Rearranging the formula:
T2 = (T1 * V2) / V1
Plugging in the given values:
T2 = (359.15 K * 6.03 L) / 6.63 L
Calculating:
T2 ≈ 326.629 K
To convert the final temperature from Kelvin to Celsius, subtract 273.15:
T2 ≈ 326.629 K - 273.15 ≈ 53.5 °C
Therefore, the balloon must be cooled to approximately 53.5 °C to reduce its volume to 6.03 L at constant pressure.