Video: Determining the Mole Ratio of CH₄ to H₂O from the Unbalanced Equation for the Complete Reaction of CH₄ and O₂

According to the following equation, what is the mole ratio of CH₄ consumed to H₂O produced? _CH₄(g) + _O₂(g) ⟶ _CO₂(g) + _ H₂O(l). [A] 1 mole CH₄ : 4 moles H₂O [B] 1 mole CH₄ : 2 moles H₂O [C] 1 mole CH₄ : 1 mole H₂O [D] 2 moles CH₄ : 1 mole H₂O [E] 4 moles CH₄ : 1 mole H₂O

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Video Transcript

According to the following equation, what is the mole ratio of CH4 consumed to H2O produced? Space CH4 gas plus space O2 gas arrow space CO2 gas plus space H2O liquid.

In this chemical equation, we have methane gas reacting with oxygen gas. These chemicals would be called the reactants in this equation. The arrow in the equation shows that products are formed. And our products here are carbon dioxide gas and water, which is present as a liquid. The letters after each chemical formula in the equation are called state symbols. “s” stands for solid, “l” for liquid, “g” for gas, and “aq” aqueous; that means it’s dissolved in water. So the equation shown here represents the complete combustion of the hydrocarbon fuel, that is, methane.

Chemical equations must balance. They must have the same number and type of each atom on both sides of the equation. In our equation here, the elements present are carbon, symbol C, hydrogen, symbol H, and oxygen, symbol O. On the reactants’ side, there’s one carbon atom present in the methane molecule. Additionally, there are four hydrogen atoms also in the methane molecule. And finally, on the reactants’ side, there are two oxygen atoms found in one oxygen molecule in our equation here.

Turning our attention to the products of this reaction, there’s one carbon atom present in a carbon dioxide molecule. Also, in the carbon dioxide molecule, there are two oxygen atoms. But we mustn’t also forget the oxygen atom found in the water molecule. This makes a total of three oxygen atoms on the products’ side. And finally, there are two hydrogen atoms found in the water molecule also. So we can clearly see that the carbon atoms are balanced on the reactants’ and products’ side of this equation. However, for the hydrogen and oxygen atoms, that’s not the case. There are different numbers of hydrogen atoms and oxygen atoms on each side of our equation. They’re not balanced.

To get our equation balanced, we need to adjust the stoichiometry of this reaction. Stoichiometry describes the quantitative relationship between the chemical substances involved in a chemical reaction. Stoichiometric coefficients will yield the ratios of the relative proportions of chemicals in the reaction. The ratio of the relative numbers of molecules involved in the reaction is often referred to as the mole ratio or the stoichiometric ratio. So we need to find the correct mole ratio to use to balance this equation.

Clearly, the carbon atoms are already balanced. And the mole ratio of methane molecules to carbon dioxide molecules can stay as one to one. One methane molecule contains four hydrogen atoms. The only way we can get four hydrogen atoms on the products’ side is by placing a balancing coefficient of two in front of the water. Placing this balancing coefficient into the space provided in the question, we can see that one methane molecule should produce one molecule of carbon dioxide and two molecules of water in the equation.

Lastly, we need to balance the oxygen atoms. On the products’ side, there are two oxygen atoms in one carbon dioxide molecule and two oxygen atoms in two water molecules. This makes a total of four oxygen atoms. We can get four oxygen atoms by placing a balancing coefficient of two in front of the oxygen molecule on the reactants’ side. The oxygens are now balanced. Transferring these balancing coefficients to the main equation, we now see that one mole of methane reacts with two moles of oxygen molecules to produce one mole of carbon dioxide and two moles of water.

So this reveals that the mole ratio of CH4 consumed to H2O produced is one mole of CH4 to two moles of H2O. One mole of CH4 to two moles of H2O is the correct answer.

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