Answer:
Write and balance the chemical reaction equation:
CH₄ + 2O₂ → CO₂ + 2H₂O
Determine the number of moles of each gas:
n(CH₄) = (1.65 atm x 2.80 L) / (0.0821 L·atm/K·mol x 298 K) = 0.201 mol
n(O₂) = (1.25 atm x 35.0 L) / (0.0821 L·atm/K·mol x 298 K) = 1.46 mol
Determine the limiting reactant (if there is one):
The balanced equation shows that 1 mole of CH₄ reacts with 2 moles of O₂. Therefore, 0.201 mol of CH₄ would require 0.402 mol of O₂ to react completely. Since there is only 1.46 mol of O₂, it is in excess and CH₄ is the limiting reactant.
Perform the stoichiometry calculation for the reaction:
From the balanced equation, we can see that 1 mole of CH₄ produces 1 mole of CO₂. Therefore, 0.201 mol of CH₄ will produce 0.201 mol of CO₂.
Determine the final volume based on the number of moles, pressure and temperature requirements:
Using the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (0.0821 L·atm/K·mol), and T is the temperature.
First, we need to convert the temperature to kelvin:
T = 125°C + 273.15 = 398.15 K
We are given the pressure of CO₂ as 2.50 atm and need to find the volume, V. The number of moles of CO₂ is 0.201 mol, which we calculated earlier. Substituting the values into the ideal gas law equation:
V = (nRT) / P
V = (0.201 mol x 0.0821 L·atm/K·mol x 398.15 K) / 2.50 atm
V = 6.44 L
Therefore, the volume of CO₂ formed at a pressure of 2.50 atm and a temperature of 125°C is 6.44 L.