Final answer:
The total volume of gas produced by the complete decomposition of 1.550 kg of trinitrotoluene (TNT), we need to use the balanced equation of the reaction and the ideal gas law. First, convert the mass of TNT to moles. Then, use the stoichiometry of the reaction to calculate the number of moles of nitrogen gas. Lastly, use the ideal gas law to calculate the volume of nitrogen gas.
Step-by-step explanation:
To calculate the total volume of gas produced by the complete decomposition of 1.550 kg of trinitrotoluene (TNT), we need to use the balanced equation of the reaction:
2 C₇H₅N₃O₆ → 3 N₂ + 5 H₂O + 7 CO + 7 C
First, we need to convert the mass of TNT to moles:
1.550 kg TNT x (1 mol TNT / 227.13 g TNT) = 6.81 mol TNT
According to the stoichiometry of the reaction, 2 moles of TNT produce 3 moles of nitrogen gas. So, with 6.81 moles of TNT, we will have:
6.81 mol TNT x (3 mol N₂ / 2 mol TNT) = 10.22 mol N₂
Next, we can use the ideal gas law to calculate the volume of nitrogen gas:
V = (nRT) / P
Where n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), T is the temperature in Kelvin, and P is the pressure in atm. Converting the temperature to Kelvin:
T = 156 °C + 273.15 = 429.15 K
Substituting the values into the equation:
V = (10.22 mol x 0.0821 L·atm/(mol·K) x 429.15 K) / 115 atm = 31.07 L
Therefore, the total volume of gas produced by the complete decomposition of 1.550 kg of trinitrotoluene is 31.07 L.