C6H12 (g) + 9 O2 (g) ----> 6CO2 (g) + 6 H2O(g)
How many L of oxygen gas is needed if we produce 5.66 L of CO2?
With all gases one can use volume in L directly as mols as a short cut.
5.66 L CO2 x (9 O2/6 CO2) = ?
3.77 L of o2
To determine the amount of oxygen gas (O2) needed, we will use the balanced chemical equation provided:
C6H12 (g) + 9 O2 (g) ----> 6 CO2 (g) + 6 H2O (g)
The equation shows a 1:9 ratio between O2 and CO2, which means that for every 1 mole of CO2 produced, 9 moles of O2 are consumed. We can use this ratio to find the number of moles of O2 needed to produce 5.66 L of CO2.
Step 1: Convert volume of CO2 to moles
Since the volume of CO2 is given in liters, we can directly use the ideal gas law at standard temperature and pressure (STP), which states that 1 mole of any ideal gas occupies 22.4 liters at 0 degrees Celsius and 1 atmosphere pressure. Therefore, we can calculate the number of moles of CO2 as follows:
5.66 L CO2 × (1 mol CO2 / 22.4 L CO2) = 0.253 moles CO2
Step 2: Use the mole ratio to find moles of O2
From the balanced chemical equation, we know that for every 6 moles of CO2 produced, 9 moles of O2 are needed. We can set up a proportion to find the number of moles of O2 required:
0.253 moles CO2 / 6 moles CO2 = x moles O2 / 9 moles O2
Cross-multiplying and solving for x, we get:
(x moles O2) = (0.253 moles CO2 × 9 moles O2) / 6 moles CO2 = 0.380 moles O2
Step 3: Convert moles of O2 to volume
Finally, we can use the ideal gas law again to convert the number of moles of O2 to volume at STP:
0.380 moles O2 × (22.4 L O2 / 1 mol O2) = 8.51 L O2
Therefore, approximately 8.51 liters of oxygen gas is needed to produce 5.66 liters of CO2 according to the given balanced chemical equation.