Aerosol cans have a label that warns the user not to use them above a certain temperature and not to dispose of them by incineration. Even an empty can contains residual gaseous propellant. For example, the residual pressure in a can is 1.16atm when it is sitting on a shelf at 23 ∘C. If the can is placed on top of the furnace where the temperature reaches the boiling point of water, what is the pressure inside the can?
(P1/T1) = (P2/T2)
To determine the pressure inside the can when it is placed on top of the furnace, we need to apply the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature in Kelvin.
First, let's convert the given temperature of 23 °C to Kelvin.
T (in Kelvin) = 23 + 273 = 296 K
Next, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (assumed constant in this case)
n = number of moles of gas (assumed constant in this case)
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature (in Kelvin)
Plugging in the values:
P₁ * V₁ = n * R * T₁
P₂ * V₁ = n * R * T₂
Since the volume of the can (V₁) and the number of moles of gas (n) are assumed to be constant, we can rewrite the equation as:
P₁ / T₁ = P₂ / T₂
Now, we can substitute the given values into the equation:
P₁ = 1.16 atm (pressure at 23 °C)
T₁ = 296 K (temperature at 23 °C)
T₂ = boiling point of water (which is 100 °C or 373 K)
P₂ / 373 K = 1.16 atm / 296 K
To find P₂, we can rearrange the equation:
P₂ = (1.16 atm / 296 K) * 373 K
Calculating:
P₂ ≈ 1.47 atm
Therefore, when the can is placed on top of the furnace, the pressure inside the can will be approximately 1.47 atm.