How much carbon dioxide gas is there in a 43.9 L container at 12.0◦C and 8.78 atm? Answer in units of g.
To determine the amount of carbon dioxide gas in the given container, you 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 given values to the appropriate units:
Volume (V) = 43.9 L
Temperature (T) = 12.0°C = 12.0 + 273.15 = 285.15 K
Pressure (P) = 8.78 atm
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plugging in the values:
n = (8.78 atm * 43.9 L) / (0.0821 L·atm/mol·K * 285.15 K)
Simplifying:
n = 383.9422 mol
Finally, to convert moles to grams, you need to know the molar mass of carbon dioxide (CO2):
1 carbon atom (12.01 g/mol) + 2 oxygen atoms (16.00 g/mol each) = 44.01 g/mol
To find the mass of the gas:
mass = n * molar mass
mass = 383.9422 mol * 44.01 g/mol
mass = 16,903.17 g
Therefore, there is approximately 16,903.17 grams of carbon dioxide gas in the 43.9 L container at 12.0°C and 8.78 atm.
Ideal Gas Law: PV=nRT
Convert temperature to Kelvin (C + 273)
Once you've done that, you have 3/4 variables. Substitute them into the ideal gas law along with the appropriate gas constant value to get n, the number of moles.
From there, use the molar mass of carbon dioxide to find the amount in grams.