Question

An aerosol can is empty, except for the propellant gas which exerts a pressure of 1.20 atm at 22 °C. If the can is thrown into a fire and heated to a temperature of 545 °C, what will be the pressure inside the hot can?

a) 2.45 atm
b) 3.60 atm
c) 4.10 atm
d) 5.20 atm

Answer 1

The pressure inside the hot aerosol can will be approximately 67.29 atm.

Step-by-step explanation:

To determine the pressure inside the hot aerosol can, we can use the ideal gas law equation: PV = nRT, where P is the initial pressure, V is the initial volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

First, convert the initial pressure of 1.20 atm to torr by multiplying by 760: 1.20 atm * 760 torr/atm = 912 torr. Next, convert the initial temperature of 22 °C to Kelvin by adding 273: 22 °C + 273 = 295 K.

Now, we can use the ideal gas law to find the pressure inside the hot can. Rearranging the equation to solve for P, we have P = (nRT)/V. Since the can is empty except for the propellant gas, the moles of gas remain the same. Plug in the known values:

P = (n * R * T_hot) / V

P = (n * R * 545 + 273) / V = (n * R * 818) / V

Finally, substitute the values: P = (n * R * 818) / V = (1 * 0.0821 * 818) / 1 = 67.2858 atm

The pressure inside the hot can will be approximately 67.29 atm.