Question

The gas left in a used aerosol can is at a pressure of atm at 27 deg C. If this can is thrown into a fire, what is the internal pressure of the gas when it's temperature reaches 927 deg C

Answer 1

To determine the final pressure of the gas inside an aerosol can when heated, use the combined gas law P1/T1 = P2/T2 with temperatures in Kelvin. The temperature increase to 927°C from 27°C could result in a dangerously high internal pressure, which is why incineration of aerosol cans is hazardous.

Step-by-step explanation:

The question involves calculating the change in pressure of a gas inside an aerosol can when it is heated from 27°C to 927°C. This scenario typically assumes that the can does not rupture or leak, which also implies the amount of gas and the volume of the can remain constant. Hence, the ideal gas law can be applied to determine the final pressure.

To calculate the final pressure, we use the combined gas law, which is a rearrangement of the ideal gas law, P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature. Assuming that the initial pressure (P1) is provided and that temperatures must be in Kelvin, we convert the temperatures from Celsius to Kelvin by adding 273.15 to each.

Here's how we would calculate it: Convert 27°C to 300.15 K and 927°C to 1200.15 K. Then, using the provided initial pressure, we can solve for P2 by rearranging the law to P2 = P1 * (T2/T1).

It is important to note that rising the temperature to such a high degree could cause the can to explode due to an extreme increase in internal pressure, which is why disposing of aerosol cans by incineration is dangerous. The precise new pressure would depend on the specified initial pressure, which the question did not include.

Answer 2

P = 4 atm

Step-by-step explanation:

In this case, we need the initial pressure which you are not providing that. I will use a pressure value of 1 atm to do this, and then, use your own value and replace it in this procedure for an accurate result.

Now, we have an aerosol can with some gas left in there at 1 atm and 27 °C. Then, the can is thrown into the fire, and the temperature raises to 927 °C. The new pressure should be higher.

In this case, the volume of the gas is not being altered, only the temperature and pressure within the can, so, we have a constant volume and we can use the Boyle's law for a constant volume, which is the following:

P₁/T₁ = P₂/T₂

From here, we can solve for P₂:

P₂ = P₁T₂/T₁

Temperature must be at Kelvin so:

T₁ = 27 + 273 = 300 K

T₂ = 927 + 273 = 1200 K

Now, replacing the data we have:

P₂ = 1 * 1200 / 300

P₂ = 4 atm