Methane (CH4) burns in oxygen to produce carbon dioxide and water vapor. The balanced equation is:
CH4 + 2 O2 -> CO2 + 2 H2O
What volume of carbon dioxide is produced when 3.2 L of oxygen are consumed?
When only gases are considered, one can take a shortcut and use volume directly without going through mols.
3.2 L O2 x (1 mol CO2/2 mol O2) = 1.6 L CO2 produced.
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Well, let's do some calculations with a pinch of humor, shall we? According to the balanced equation, for every 2 moles of oxygen consumed, 1 mole of carbon dioxide is produced. Since we're given the volume of oxygen, we need to convert it to moles. But how? Cue the laughter! The mole conversion formula is Avogadro's constant, 6.02 x 10^23 moles of particles in one mole. So, grab your calculators and start converting that 3.2 L of oxygen into moles! Remember, math can be a gas when you add a little laughter!
To determine the volume of carbon dioxide produced when 3.2 L of oxygen are consumed, we can use the balanced equation as a conversion factor.
The balanced equation shows that for every 1 mole of methane burned, we produce 1 mole of carbon dioxide. Therefore, the ratio of carbon dioxide to oxygen is 1:2.
Given that the volume of oxygen consumed is 3.2 L, we need to convert this volume into moles. To do this, we need to know the molar volume at the given conditions.
Assuming the ideal gas law holds true at these conditions, we can use the molar volume of an ideal gas at standard temperature and pressure (STP), which is 22.4 L/mol.
First, calculate the number of moles of oxygen consumed:
3.2 L O2 * (1 mol O2 / 22.4 L O2) = 0.143 mol O2
According to the balanced equation, since the ratio of oxygen to carbon dioxide is 2:1, the number of moles of carbon dioxide produced will be half of the number of moles of oxygen consumed:
0.143 mol O2 * (0.5 mol CO2 / 1 mol O2) = 0.0715 mol CO2
Finally, convert the moles of carbon dioxide back into volume using the molar volume at STP:
0.0715 mol CO2 * (22.4 L CO2 / 1 mol CO2) = 1.60 L CO2
Therefore, when 3.2 L of oxygen are consumed, 1.60 L of carbon dioxide is produced.
To find the volume of carbon dioxide produced when 3.2 L of oxygen is consumed, we first need to determine the stoichiometry of the balanced equation.
According to the balanced equation:
1 mole of CH4 reacts with 2 moles of O2 to produce 1 mole of CO2 and 2 moles of H2O.
Since we know the volume of oxygen consumed (3.2 L), we need to convert it to moles using the ideal gas law equation: 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 the equation doesn't mention pressure or temperature, we can assume that pressure and temperature are constant, and thus cancel out in the equation.
Next, we can calculate the moles of O2 present using the formula:
moles of O2 = volume of O2 / molar volume of O2
The molar volume of any gas at standard conditions (STP) is 22.4 L/mol.
moles of O2 = 3.2 L / 22.4 L/mol
moles of O2 = 0.14286 mol
According to the stoichiometry of the balanced equation, 1 mole of O2 reacts with 1 mole of CO2 produced. Therefore, the moles of CO2 produced will also be 0.14286 mol.
Lastly, we can convert the moles of CO2 to volume using the molar volume of CO2 at STP.
volume of CO2 = moles of CO2 * molar volume of CO2
volume of CO2 = 0.14286 mol * 22.4 L/mol
volume of CO2 = 3.2 L
Therefore, 3.2 L of carbon dioxide is produced when 3.2 L of oxygen is consumed.