Assuming all volume measurements are made at the same temperature and pressure, how many liters of carbon dioxide gas can be produced when 12.8 liters of oxygen gas react with excess carbon monoxide? Show all of the work used to solve this problem.
To determine how many liters of carbon dioxide gas can be produced when 12.8 liters of oxygen gas react with excess carbon monoxide, we first need to determine the balanced chemical equation for the reaction between oxygen gas (O2) and carbon monoxide (CO).
The balanced chemical equation for the reaction is:
2 CO + O2 -> 2 CO2
This means that for every 2 moles of carbon monoxide reacting with 1 mole of oxygen gas, we will produce 2 moles of carbon dioxide.
To solve this problem, we need to follow these steps:
Step 1: Convert the given volume of oxygen gas (12.8 L) to moles using the ideal gas law equation:
PV = nRT
Where:
P = pressure (which we assume to be constant)
V = volume of gas (12.8 L)
n = number of moles of oxygen gas (what we want to find)
R = ideal gas constant
T = temperature (which we assume to be constant)
From the equation, we can rearrange it to solve for n:
n = PV / RT
Using the known values for pressure and temperature, we can calculate the number of moles of oxygen gas:
n = (P * V) / (R * T)
Step 2: Since the reaction equation tells us that 1 mole of oxygen gas reacts with 2 moles of carbon monoxide, we can use the stoichiometry of the reaction to determine the number of moles of carbon monoxide.
In this case, since carbon monoxide is in excess, it means that we have an unlimited amount of it available, and we only need to consider the limiting reactant, which is oxygen gas.
So, the number of moles of carbon monoxide is equal to half the number of moles of oxygen gas.
moles of carbon monoxide = 1/2 * moles of oxygen gas
Step 3: Finally, we can convert the moles of carbon monoxide to liters of carbon dioxide gas, using the balanced chemical equation to determine the stoichiometry between the two gases.
From the reaction equation, we know that 2 moles of carbon monoxide react to produce 2 moles of carbon dioxide.
Since the molar volume of any ideal gas is 22.4 L/mol at standard temperature and pressure (STP), we can use this value to convert moles to liters.
liters of carbon dioxide gas = moles of carbon monoxide * molar volume
Now, we can calculate the value:
1. Convert liters of oxygen gas to moles:
n = (P * V) / (R * T)
2. Determine the number of moles of carbon monoxide:
moles of carbon monoxide = 1/2 * moles of oxygen gas
3. Convert moles of carbon monoxide to liters of carbon dioxide gas:
liters of carbon dioxide gas = moles of carbon monoxide * molar volume
By following these steps, you can determine the number of liters of carbon dioxide gas that can be produced when 12.8 liters of oxygen gas react with excess carbon monoxide.
With all gases one may use a shortcut by using liters and not converting to moles.
1. Write and balance the equation.
2. Using the coefficients in the balanced equation, convert 12.8 L O2 to liters CO2.