A bottle with a open mouth contains air atººººººººº 47º𝐶. The temperature to which the bottle must be heated so that 1/5th of the mass of air leaves the bottle is

This problem can be solved using the ideal gas law, which states that the pressure times the volume of a gas is proportional to the number of moles of the gas times the temperature of the gas (PV = nRT).

In this case, we are trying to find the temperature at which 1/5th of the air leaves the bottle. This means that the number of moles of air in the bottle decreases to 4/5th of its original amount.

Since the bottle is open, we can assume that the pressure remains constant. Therefore, the volume of the gas is proportional to the number of moles times the temperature (V = nT).

If we let the original temperature be T1 (which is 47ºC or 320.15 K when converted to Kelvin) and the final temperature be T2, and the original number of moles be n and the final number of moles be 4n/5, we can set up the following equation:

nT1 = (4n/5)T2

Solving for T2 gives:

T2 = 5T1/4 = 5*320.15/4 = 400.1875 K

Therefore, the bottle must be heated to approximately 400.19 K (or 127.04ºC when converted back to Celsius) for 1/5th of the air to leave the bottle.