All volume measurements are carried out at the same temperature and pressure. If 20.0 L of O2 (g) are allowed to completely react with a sample of pure CH4 (g) in a combustion process producing CO2 (g) as the only carbon-containing product, what is the maximum volume of CH4 (g) that can be consumed in that reaction?

CH4 + 2O2 ==> CO2 + 2H2O

Convert 20 L O2 to L CH4.
20 L CO2 x (1 mole CH4/2 moles O2) = 20 x (1/2) = 10 L CH4.

To determine the maximum volume of CH4 gas that can be consumed in the reaction, we need to use the stoichiometry of the balanced equation and the ideal gas law.

1. Write the balanced equation for the combustion of CH4:
CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O (g)

2. From the balanced equation, we can see that one mole of CH4 reacts with two moles of O2. Therefore, the mole ratio between CH4 and O2 is 1:2.

3. Convert the given volume of O2 gas to moles:
Using the ideal gas law, PV = nRT, we can calculate the number of moles of O2.
Assuming the temperature and pressure are constant, we can rearrange the equation to find moles:
n = PV / RT = (20.0 L) / (22.414 L/mol·K) = 0.892 mol

4. From the mole ratio, we know that for every one mole of CH4, two moles of O2 are required. Therefore, the maximum mole ratio between CH4 and O2 is 1:0.5.

5. Use the mole ratio to calculate the maximum number of moles of CH4 that can be consumed:
Moles of CH4 = Moles of O2 × (1 mol CH4 / 2 mol O2) = 0.892 mol × (1 mol CH4 / 2 mol O2) = 0.446 mol

6. Convert the moles of CH4 back into volume:
Using the ideal gas law, we can calculate the volume of CH4 gas.
V = nRT / P = (0.446 mol) × (22.414 L/mol·K) / 1 atm = 9.999 L

Therefore, the maximum volume of CH4 gas that can be consumed in the reaction is approximately 9.999 L.

To determine the maximum volume of CH4 (g) consumed in the reaction, we need to use stoichiometry and the ideal gas law.

First, let's write the balanced chemical equation for the combustion of CH4:

CH4 (g) + 2O2 (g) -> CO2 (g) + 2H2O (g)

According to the equation, 1 mole of CH4 reacts with 2 moles of O2 to produce 1 mole of CO2. Thus, the stoichiometric ratio between CH4 and CO2 is 1:1.

Given that 20.0 L of O2 (g) is allowed to react, we can use the ideal gas law to find the number of moles of O2:

PV = nRT

Assuming the temperature and pressure are constant, we can use the formula in terms of moles:

n = PV / RT

where P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature.

Now, let's calculate the number of moles of O2:

nO2 = (20.0 L)(1 atm) / (0.0821 L·atm/mol·K)(T)

Since the temperature is not given, we don't have enough information to calculate the exact number of moles. However, the number of moles of CH4 consumed will be the same as the number of moles of O2 because of the stoichiometry between the two gases.

So, the maximum volume of CH4 that can be consumed in the reaction will also be 20.0 L.

However, please note that to get an accurate answer, we would need to know the temperature and pressure at which the reaction is taking place. Without those values, we can't calculate the actual number of moles or the exact volume of CH4 consumed.