Question
What mass of CO2 is needed to fill an 80.0 L tank to a pressure of 150.0 atm at 27.0°C?
Answers
GPT 3.5
To calculate the mass of CO2 needed to fill the tank, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T = 27.0°C + 273.15 = 300.15 K
Now, we can rearrange the equation to solve for the number of moles:
n = (PV) / (RT)
n = (150.0 atm * 80.0 L) / (0.0821 L*atm/mol*K * 300.15 K)
n = 497.6 moles
Next, we need to calculate the mass using the molar mass of CO2:
Molar mass of CO2 = 12.01 + 2(16.00) = 44.01 g/mol
Mass = n * molar mass
Mass = 497.6 moles * 44.01 g/mol
Mass = 21914.18 g
Therefore, approximately 21,914 grams (or 21.914 kg) of CO2 is needed to fill the 80.0 L tank to a pressure of 150.0 atm at 27.0°C.
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L*atm/mol*K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T = 27.0°C + 273.15 = 300.15 K
Now, we can rearrange the equation to solve for the number of moles:
n = (PV) / (RT)
n = (150.0 atm * 80.0 L) / (0.0821 L*atm/mol*K * 300.15 K)
n = 497.6 moles
Next, we need to calculate the mass using the molar mass of CO2:
Molar mass of CO2 = 12.01 + 2(16.00) = 44.01 g/mol
Mass = n * molar mass
Mass = 497.6 moles * 44.01 g/mol
Mass = 21914.18 g
Therefore, approximately 21,914 grams (or 21.914 kg) of CO2 is needed to fill the 80.0 L tank to a pressure of 150.0 atm at 27.0°C.