Two reactions that occur in the production of
iron (Fe) are
2 C + O2 → 2 CO
followed by
Fe2O3 + 3 CO → 2 Fe + 3 CO2 .
Note that the carbon monoxide (CO) formed
in the first reaction is then used in the second
reaction. According to these equations, how
much oxygen (O2) is required to produce 800
moles of Fe?
1. 300 mol
2. 600 mol
3. 1200 mol
4. None of these
5. 900 mol
2C + O2 → 2CO
Fe2O3 + 3 CO → 2 Fe + 3 CO2 .
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From eqn one. 1 mol O2 = 2 mols CO
From eqn two. 3 mols CO = 2 mols Fe
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We get mols CO equal in the two equations. Multiply equation two by 2/3 like this. 3 mols CO x 2/3 = 2 mols Fe x 2/3 or
2 mols CO = 4/3 mol Fe. Then let me rewrite the two equations like this.
eqn one still is 1 mol O2 = 2 mols CO and
equation two is 2 mols CO = 4/3 mol Fe. Since both eqn 1 and equation 2 equal 2 mols CO, then 1 mol O2 = 4/3 mol Fe, You want 800 mols Fe.
So 800 moles Fe x (1 mol O2/4/3 mol Fe) = 800 x 3/4 = 600 mols O2 required.
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Let's check that.
equation one tells that starting with 600 moles O2 will produce 1200 mols of CO. Then equation two tells us that 1200 moles CO will produce 1200 x 2/3 = 2400/3 or 800 mols Fe. Yay! It checks.
To determine how much oxygen (O2) is required to produce 800 moles of Fe, we can start by examining the balanced chemical equations given.
The first reaction is: 2 C + O2 → 2 CO
From this equation, we can see that for every 2 moles of carbon (C) reacted, 1 mole of oxygen (O2) is required. Therefore, the second reaction will provide us with the amount of CO produced in the first reaction (which is then used in the second reaction).
The second reaction is: Fe2O3 + 3 CO → 2 Fe + 3 CO2
From this equation, we can see that for every 3 moles of CO, 1 mole of Fe2O3 is reacted. Given that we have 800 moles of Fe, we need to determine how many moles of CO are required to produce 800 moles of Fe.
In the second reaction, we have a ratio of 3 moles of CO to 2 moles of Fe. This means that for every 2 moles of Fe, we need 3 moles of CO.
To calculate the amount of CO required, we can set up a proportion:
(2 moles Fe) / (3 moles CO) = (800 moles Fe) / x moles CO
Solving for x, we get:
x = (800 moles Fe) * (3 moles CO) / (2 moles Fe)
x = 1200 moles CO
Therefore, 1200 moles of carbon monoxide (CO) are required to produce 800 moles of iron (Fe).
Hence, the correct answer is 3. 1200 mol.