A can of soda has the total volume of 350ml. This can is open and only contains atmospheric air, and is placed within a furnace
100 ° C. After the can achieve this reduced temperature at 25 ° C. With decreasing temperature, there is a reduction of the internal pressure that can lead to an implosion. Based on the foregoing, calculate the pressure inside the can and the final volume
To calculate the pressure inside the can and the final volume, we can make use of the Ideal Gas Law. The Ideal Gas Law equation is:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles of gas
R = Ideal gas constant
T = Temperature (in Kelvin)
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature, Ti = 100°C + 273.15 = 373.15K
Final temperature, Tf = 25°C + 273.15 = 298.15K
Since the can only contains atmospheric air, we can assume it is mostly composed of nitrogen gas (N₂). The molar mass of nitrogen is approximately 28 g/mol.
To calculate the number of moles of gas, we need to know the mass of the gas. Given that the volume of the can is 350 ml and the density of air at room temperature and pressure is about 1.23 kg/m³, we can calculate the mass of the air inside the can.
Mass = density * volume
Mass = 1.23 kg/m³ * 0.00035 m³ = 4.305 g
Next, we convert the mass of air to moles:
moles = mass / molar mass
moles = 4.305 g / 28 g/mol = 0.15375 mol
Now, we can calculate the initial pressure inside the can using the initial temperature:
PV = nRT
P * 0.00035 L = 0.15375 mol * 0.0821 L·atm/mol·K * 373.15 K
P = (0.15375 mol * 0.0821 L·atm/mol·K * 373.15 K) / 0.00035 L
P = 10.36 atm
Therefore, the initial pressure inside the can at 100°C is approximately 10.36 atm.
To find the final volume, we can rearrange the Ideal Gas Law equation:
Vf = (n * R * Tf) / Pf
Where:
Vf = final volume
n = number of moles
R = Ideal gas constant
Tf = final temperature (in Kelvin)
Pf = final pressure (which we need to calculate)
Since the can is open and the air inside is exposed to atmospheric pressure, we can assume the final pressure inside the can is approximately equal to atmospheric pressure, which is 1 atm.
Vf = (0.15375 mol * 0.0821 L·atm/mol·K * 298.15 K) / 1 atm
Vf = 3.858 L
Therefore, the final volume inside the can at 25°C is approximately 3.858 liters.
To summarize:
- The pressure inside the can at 100°C is approximately 10.36 atm.
- The final volume inside the can at 25°C is approximately 3.858 liters.