a 2L container is charged with 2atm of O2 at 298 Kelvin.

Ch4(g) + 2O2(g) --> CO2(g) + 2H20(g)

calculate the partial pressure of methane needed to react completely with the O2 in the vessel. What is the total pressure after the reaction is complete if the temperature increased to 750 Celcius?

To calculate the partial pressure of methane (CH4) needed to react completely with the O2 in the vessel, we can use the ideal gas law equation:

PV = nRT

Where:
P is the pressure of the gas
V is the volume of the container
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature in Kelvin

First, let's calculate the number of moles of O2 in the container. Given that the container has a volume of 2 liters and a pressure of 2 atm, we can rearrange the ideal gas law equation to solve for n:

n(O2) = PV / RT

n(O2) = (2 atm) * (2 L) / (0.0821 L·atm·mol^(-1)·K^(-1)) * (298 K)

n(O2) ≈ 0.196 mol

According to the balanced chemical equation provided, the stoichiometric ratio between CH4 and O2 is 1:2. This means that for every 2 moles of O2, we need 1 mole of CH4 to react completely.

n(CH4) = n(O2) / 2

n(CH4) = 0.196 mol / 2

n(CH4) ≈ 0.098 mol

Now we can calculate the partial pressure of methane (CH4). Since we know the volume of the container (2 liters) and the number of moles of methane (0.098 mol), we can rearrange the ideal gas law to solve for the pressure:

P(CH4) = (n(CH4) * R * T) / V

P(CH4) = (0.098 mol) * (0.0821 L·atm·mol^(-1)·K^(-1)) * (298 K) / (2 L)

P(CH4) ≈ 1.20 atm

Now, let's calculate the total pressure after the reaction is complete when the temperature increases to 750 degrees Celsius. We need to convert the temperature from Celsius to Kelvin:

T(Kelvin) = temperature(Celsius) + 273.15

T(Kelvin) = 750°C + 273.15

T(Kelvin) = 1023.15 K

Using the combined gas law formula:

P1V1 / T1 = P2V2 / T2

Where:
P1 is the initial pressure
V1 is the initial volume
T1 is the initial temperature
P2 is the final pressure
V2 is the final volume
T2 is the final temperature

Initially, the pressure in the container is 2 atm, and the volume is 2 liters. We can plug in these values and solve for P2:

(2 atm * 2 L) / (298 K) = (P2 * 2 L) / (1023.15 K)

P2 = (2 atm * 2 L * 1023.15 K) / (2 L * 298 K)

P2 ≈ 13.68 atm

Therefore, the total pressure after the reaction is complete and the temperature increases to 750 degrees Celsius is approximately 13.68 atm.

Use PV = nRT

You know P, V, R, and T, calculate n for oxygen.
That allows you to calculate CH4 moles and from there moles CO2 and moles H2O.
Then calculate total P from new conditions for PV = nRT.