Just having some trouble with this chemistry problem.. Thanks for help!
Toxic carbon monoxide (CO) gas is produced when fossil fuels such as petroleum burn without enough oxygen. The CO can eventually be converted to CO2 in the atmosphere. Automobile catalytic converters are designed to speed up this conversion:
Carbon monoxide gas + Oxygen gas → Carbon Dioxide Gas
a. Write the balanced equation for this conversion.
b. How many moles of oxygen gas would be needed to convert 50.0 mol of carbon monoxide to carbon dioxide?
c. What volume of oxygen gas would be needed to convert with 968 L of carbon monoxide? (assume both gases are at the same temperature and pressure.)
a. Write the balanced equation for this conversion.
2CO + O2 ==> 2CO2
b. How many moles of oxygen gas would be needed to convert 50.0 mol of carbon monoxide to carbon dioxide?
50.0 mol CO x (1 mol O2/2 mol CO) = ? mol CO2
c. What volume of oxygen gas would be needed to convert with 968 L of carbon monoxide? (assume both gases are at the same temperature and pressure.)
When dealing with gases one can use L directly without converting to mols.
968 L CO x (1 mol O2/2 mol CO) = ? L O2 needed.
a. To write the balanced equation for this conversion, we need to ensure that the number of atoms of each element is the same on both sides of the equation. Let's start with the carbon atoms. Since there is only one carbon atom in carbon monoxide and one carbon atom in carbon dioxide, the equation can start as:
CO + O2 → CO2
Next, let's balance the oxygen atoms. There are two oxygen atoms in carbon dioxide, so we need two oxygen molecules on the left-hand side of the equation. The balanced equation becomes:
2CO + O2 → 2CO2
Now, all the elements are balanced, and the equation is balanced.
b. In order to find the number of moles of oxygen gas needed to convert 50.0 mol of carbon monoxide to carbon dioxide, we need to use the coefficients in the balanced equation. In the balanced equation:
2CO + O2 → 2CO2
We can see that the ratio of carbon monoxide to oxygen gas is 2:1. Therefore, for every 2 moles of carbon monoxide, we need 1 mole of oxygen gas. Since we have 50.0 mol of carbon monoxide, we divide it by 2 to find the number of moles of oxygen gas:
50.0 mol CO / 2 mol CO = 25.0 mol O2
So, 25.0 moles of oxygen gas would be needed to convert 50.0 moles of carbon monoxide to carbon dioxide.
c. To find the volume of oxygen gas needed, we can use the ideal gas law equation, which states PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Since we are assuming both gases are at the same temperature and pressure, we can use the equation to find the volume of oxygen gas.
First, we need to find the number of moles of oxygen gas using the balanced equation:
2CO + O2 → 2CO2
From the balanced equation, we know that for every 2 moles of carbon monoxide, we need 1 mole of oxygen gas. So, the number of moles of oxygen gas is half the number of moles of carbon monoxide.
Now, let's use the ideal gas law equation to find the volume of oxygen gas:
V(O2) = (n(O2) * R * T) / P
Since we are assuming the gases are at the same temperature and pressure, we can simplify the equation to:
V(O2) = n(O2) * constant
So, the volume of oxygen gas needed would be equal to half the volume of carbon monoxide:
V(O2) = 968 L CO / 2 = 484 L O2
Therefore, 484 liters of oxygen gas would be needed to convert 968 liters of carbon monoxide to carbon dioxide.
a. The balanced equation for the conversion of carbon monoxide to carbon dioxide is:
2 CO + O2 -> 2 CO2
b. To determine the number of moles of oxygen gas required to convert 50.0 mol of carbon monoxide, we refer to the balanced equation. From the equation, we can see that for every 2 moles of carbon monoxide, we need 1 mole of oxygen gas.
Therefore, we can set up the following proportion:
2 moles of CO / 1 mole of O2 = 50.0 moles of CO / x moles of O2
Simplifying the proportion:
2 / 1 = 50.0 / x
Cross-multiplying:
2x = 50.0
Dividing both sides by 2:
x = 25.0 moles of O2
So, 25.0 moles of oxygen gas would be needed to convert 50.0 moles of carbon monoxide to carbon dioxide.
c. To determine the volume of oxygen gas needed to convert 968 L of carbon monoxide, we need to use the molar volume of gases at the same temperature and pressure. At standard temperature and pressure (STP), the molar volume of any ideal gas is 22.4 L.
Using this information, we can set up the following proportion:
22.4 L of CO / 2 moles of CO = 968 L of CO / x moles of O2
Simplifying the proportion:
22.4 / 2 = 968 / x
Cross-multiplying:
22.4x = 1936
Dividing both sides by 22.4:
x ≈ 86.4 L/mol
Therefore, approximately 86.4 liters of oxygen gas would be required to convert with 968 L of carbon monoxide.