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A sample of methane gas (CH₂) having a volume of 2.80 L at 25 °C and 1.65 atm was mixed with a

sample of oxygen gas having a volume of 35.0 L and 1.25 atm. The mixture was then ignited to form carbon
dioxide and water. Calculate the volume of CO₂ formed at a pressure of 2.50 atm and a temperature of 125
°C.
Recommended Steps:
1. Write and Balance the chemical reaction equation
2. Determine the number of moles of each gas
3. Determine the limiting reactant (if there is one)
4. Perform the stoichiometry calculation for the reaction
5. Determine the final volume based on the number of moles, pressure and temperature requirements.

User Farenorth
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1 Answer

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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.
User Marco
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