Aerosol cans carry clear warnings against incineration because of the high pressures that can develop upon heating. Suppose a can contains a residual amount of gas at a pressure of 755 mm Hg and a temperature of 25 °C. What would the pressure be if the can were heated to 1155 °C?
4.76 atm
To determine the pressure inside the can when heated to 1155 °C, we can use the ideal gas law. The ideal gas law equation is given as:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = gas constant
T = temperature in Kelvin
First, we need to convert the initial temperature of 25 °C to Kelvin. Kelvin temperature is obtained by adding 273.15 to the Celsius temperature. So 25 °C + 273.15 = 298.15 K.
Next, we need to calculate the number of moles of gas in the can. This can be done using the ideal gas law rearranged to solve for n:
n = PV / RT
Given:
P1 = 755 mm Hg
V1 = volume (which we assume to be constant)
T1 = 298.15 K
Now, we need to convert the temperature of 1155 °C to Kelvin. 1155 °C + 273.15 = 1428.15 K.
Using the ideal gas law, we can now calculate the pressure at the new temperature:
n = (P1 * V1) / (R * T1)
Let's assume the volume remains constant, so V1 = V2. Therefore, we can simplify the equation:
n = P1 / (R * T1)
Now, calculate the pressure at the new temperature:
P2 = n * R * T2
Given:
T2 = 1428.15 K
Substituting the values, we can calculate the pressure (P2):
P2 = (P1 / (R * T1)) * (R * T2)
Once you have plugged in the values into the equation and performed the calculations, you will find the pressure (P2) inside the can when heated to 1155 °C.