Question

For the balanced chemical equation for the combination reaction of hydrogen gas and oxygen gas $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) $$ explain why we know that \(2 \mathrm{~g}\) of \(\mathrm{H}_{2}\) reacting with \(1 \mathrm{~g}\) of \(\mathrm{O}_{2}\) will not result in the production of \(2 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\)

Short answer

In the given balanced chemical equation, 2 moles of H₂ react with 1 mole of O₂ to produce 2 moles of H₂O. We have 2 grams of H₂, which is equivalent to 1 mole, and 1 gram of O₂, which is equivalent to 0.03125 moles. Since the required ratio of H₂ to O₂ is 2:1, oxygen is the limiting reactant in this case. The amount of H₂O produced depends on the amount of O₂ present, which will produce 0.0625 moles of H₂O. This corresponds to 1.125 grams of H₂O, not 2 grams as mentioned in the question. This is because the limiting reactant (O₂) determines the amount of product formed.

Step-by-step solution

1. Find molar mass of each element involved

: First, we need to find the molar mass of each element involved in the reaction. The molar mass of Hydrogen (H) is approximately 1 g/mol, and the molar mass of Oxygen (O) is approximately 16 g/mol.

2. Calculate molar mass of involved molecules

: For hydrogen gas (H₂) molecule, there are two hydrogen atoms, so the molar mass is \(2\times1 = 2\)g/mol. For oxygen gas (O₂) molecule, there are two oxygen atoms, so the molar mass is \(2\times16 = 32\)g/mol. For water (H₂O) molecule, there are two hydrogen atoms and one oxygen atom, so the molar mass is \((2\times1)+(1\times16) = 18\) g/mol.

3. Determine moles of reactants

: According to the problem, we have 2 grams of H₂ and 1 gram of O₂. To find the number of moles of each reactant, we divide the mass by their respective molar masses. For H₂: \(\frac{2}{2} = 1\) mole, and for O₂: \(\frac{1}{32} = 0.03125\) mole.

4. Analyze reactants' ratios

: From the balanced equation: 2 H₂(g) + O₂(g) -> 2 H₂O(g), we can see that 2 moles of H₂ react with 1 mole of O₂. We have 1 mole of H₂ and 0.03125 moles of O₂.

5. Identify limiting reactant

: Since the required ratio of H₂ to O₂ is 2:1, and we have more than the required amount of H₂ relative to O₂, O₂ is the limiting reactant in this reaction. This means that the amount of H₂O formed will depend on the amount of O₂ present.

6. Calculate the amount of H₂O produced

: According to the balanced equation, 1 mole of O₂ will produce 2 moles of H₂O. Since we have 0.03125 moles of O₂, we will get \(2\times0.03125 = 0.0625\) moles of H₂O.

7. Calculate mass of H₂O produced

: Since the molar mass of H₂O is 18 g/mol, the mass of H₂O produced is \(0.0625\times18 = 1.125\) g.

8. Conclusion

: According to our calculations, 2 grams of H₂ reacting with 1 gram of O₂ will result in the production of 1.125 grams of H₂O, not 2 grams of H₂O. This is due to the limiting reactant (O₂), which determines the amount of product formed.

Key concepts

Limiting Reactant

Understanding the concept of the limiting reactant is crucial in chemical reactions because it determines the maximum amount of product that can be formed. The limiting reactant is the substance that is completely used up first during the reaction, thus limiting the amount of products formed. Imagine having a car factory with plenty of car doors but only a few tires. You can only build as many complete cars as you have tires, no matter how many doors you have. In the given problem of hydrogen and oxygen combining to form water, the amount of oxygen is not sufficient to react with all the available hydrogen, making oxygen the limiting reactant.

In any chemical reaction, identifying the limiting reactant is a key step. You compare the mole ratio of the reactants used in the reaction to the mole ratio given in the balanced chemical equation. If the mole ratio of one reactant is less than the ratio in the balanced equation, that reactant is the limiting one. Once the limiting reactant is consumed, the reaction stops, even if other reactants are still present.

Molar Mass

The molar mass of a substance is the mass in grams of 1 mole of that substance. One mole of any substance contains exactly 6.022 x 10²³ particles (Avogadro's number), which could be atoms, molecules, ions, or electrons. The molar mass is an essential concept in stoichiometry as it links the mass of a substance to the amount in moles, which is vital for calculating reactant or product quantities.

To find the molar mass, you look at the molecular formula and add up the atomic masses of all the atoms in the molecule. For instance, for H₂O, you have two hydrogen atoms and one oxygen atom. Since the atomic mass of hydrogen is approximately 1 g/mol and oxygen is 16 g/mol, the molar mass of water becomes \(2\times1)+(1\times16) = 18\) g/mol. It's like making a recipe where you need to know the weight of the ingredients to determine how much of each you need for the desired outcome.

Balanced Chemical Equations

Chemical equations must be balanced to obey the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. Thus, a balanced chemical equation has the same number of atoms of each element in the reactants and products. Balancing a chemical equation is like balancing scales; what you put on one side (reactants) must equal what's on the other side (products) in terms of atom count and mass.

A balanced chemical equation ensures that all atoms are accounted for during the reaction, and it provides crucial information about the relationship between reactants and products. For example, the equation \(2 \text{H}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{H}_{2}\text{O}(g)\) represents the reaction between hydrogen and oxygen to form water. It shows that two molecules of hydrogen gas react with one molecule of oxygen gas to produce two molecules of water. In the context of the exercise, this ratio is important for determining which reactant will run out first and thus dictate the amount of product formed.