A steel tank contains carbon dioxide at 34 celsius and is at a pressure of 13.0 atm. Determine the internal gas pressure when the tank and its contents are heated to 100 celsius
P1/T1 = P2/T2 at constant V.
Do I need to convert the temperature from Celsius to Kelvin for this equation. The answers are multiple choice and there is one for it using both. Isn't kelvin always used for these type of calculations?
To determine the internal gas pressure when the tank and its contents are heated to 100 degrees Celsius, we can use the ideal gas law equation, which is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant (0.0821 L*atm/(mol*K))
T = Temperature in Kelvin
First, let's convert the given temperatures to Kelvin:
Initial temperature (T1) = 34 °C + 273.15 = 307.15 K
Final temperature (T2) = 100 °C + 273.15 = 373.15 K
Now, let's assume that the volume (V) of the steel tank remains constant. Therefore, we can write the equation as follows:
P1 * V = n * R * T1 -- (Equation 1)
P2 * V = n * R * T2 -- (Equation 2)
Since the number of moles (n) remains constant, we can simplify the equations as:
P1 / T1 = P2 / T2
Now, let's substitute the given values into the equation:
P1 = 13.0 atm
T1 = 307.15 K
T2 = 373.15 K
Plugging in the values, we get:
13.0 atm / 307.15 K = P2 / 373.15 K
To find P2, we can cross-multiply and solve for P2:
P2 * 307.15 K = 13.0 atm * 373.15 K
P2 * 307.15 K = 4,845.95 atm * K
Dividing both sides by 307.15 K:
P2 = 4,845.95 atm * K / 307.15 K
P2 ≈ 15.8 atm
Therefore, the internal gas pressure when the tank and its contents are heated to 100 degrees Celsius is approximately 15.8 atm.
To determine the internal gas pressure when the tank and its contents are heated to 100 degrees Celsius, you can use the Ideal Gas Law, which states that:
PV = nRT
Where:
P = Pressure of the gas
V = Volume of the gas
n = Number of moles of gas
R = Ideal Gas Constant (0.0821 L·atm/mol·K)
T = Temperature of the gas in Kelvin
First, convert the temperatures from Celsius to Kelvin:
Initial temperature (T1) = 34 degrees Celsius + 273.15 = 307.15 K
Final temperature (T2) = 100 degrees Celsius + 273.15 = 373.15 K
Since we are dealing with the same tank and its contents before and after heating, the volume (V) and the number of moles (n) are constant. Therefore, we can rewrite the equation as:
P1 / T1 = P2 / T2
Where:
P1 = Initial pressure of the gas (13.0 atm)
T1 = Initial temperature (307.15 K)
P2 = Final pressure of the gas (What we need to find)
T2 = Final temperature (373.15 K)
Now, we can rearrange the equation to solve for P2:
P2 = (P1 * T2) / T1
Substituting the given values:
P2 = (13.0 atm * 373.15 K) / 307.15 K
P2 ≈ 15.85 atm
Therefore, the internal gas pressure when the tank and its contents are heated to 100 degrees Celsius is approximately 15.85 atm.