if 10.5 moles of CH4 react with oxygen, what is the volume of CO2 (in liters) produced at 20.9 degrees celsius and 0.951 atm?
CH4 + 2O2 --> CO2 + 2H2O
mols CH4 = 10.4
Using the coefficients in the balanced equation, convert mols CH4 to mols CO2.
Then use PV = nRT and convert mols CO2 at the conditions listed to volume in L.
To find the volume of CO2 produced, we need to use the balanced chemical equation for the reaction of CH4 with oxygen:
CH4 + 2O2 → CO2 + 2H2O
According to the balanced equation, one mole of CH4 produces one mole of CO2.
Given that we have 10.5 moles of CH4, we can conclude that we will have an equal number of moles of CO2.
Now, we will use the ideal gas law equation to find the volume of CO2.
PV = nRT
Where:
P is the pressure (0.951 atm),
V is the volume of the gas,
n is the number of moles (10.5 moles),
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature in Kelvin.
First, we need to convert the temperature from Celsius to Kelvin.
T(K) = T(°C) + 273.15
T(K) = 20.9 + 273.15
T(K) = 294.05 K
Now, we can substitute the values into the ideal gas law equation and solve for V:
(0.951 atm) * V = (10.5 mol) * (0.0821 L·atm/(mol·K)) * (294.05 K)
V = (10.5 mol) * (0.0821 L·atm/(mol·K)) * (294.05 K) / (0.951 atm)
V ≈ 235.66 L
Therefore, the volume of CO2 produced is approximately 235.66 liters.
To find the volume of CO2 produced, we first need to determine the balanced chemical equation for the reaction between CH4 and oxygen (O2):
CH4 + 2O2 -> CO2 + 2H2O
According to the balanced equation, 1 mole of CH4 produces 1 mole of CO2.
Given that we have 10.5 moles of CH4, we can conclude that the same amount of CO2 will be produced.
To calculate the volume, we will use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm (0.951 atm in this case)
V = volume in liters (unknown)
n = number of moles (10.5 moles in this case)
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (20.9 °C + 273.15 = 294.05 K)
Rearranging the equation to solve for V:
V = (nRT) / P
V = (10.5 moles * 0.0821 L·atm/mol·K * 294.05 K) / 0.951 atm
Calculating this expression will yield the volume of CO2 produced in liters.