(a) Consider the combustion of hydrogen, 2 H21g2 + O21g2 ¡ 2 H2O1g2. If hydrogen is burning at the rate of 0.48 mol>s, what is the rate of consumption of oxygen? What is the rate of formation of water vapor?

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Step 1: Write down the balanced chemical equation for the combustion of hydrogen. It is given as 2 H2(g) + O2(g) → 2 H2O(g).

Step 2: From the balanced equation, we can see that the stoichiometric ratio of hydrogen to oxygen to water is 2:1:2. This means that for every 2 moles of hydrogen consumed, 1 mole of oxygen is consumed and 2 moles of water are produced.

Step 3: Given that hydrogen is burning at the rate of 0.48 mol/s, we can use the stoichiometric ratio to find the rate of consumption of oxygen. Since the ratio of hydrogen to oxygen is 2:1, the rate of consumption of oxygen will be half of the rate of consumption of hydrogen.

Step 4: Similarly, we can find the rate of formation of water. Since the ratio of hydrogen to water is 2:2 or 1:1, the rate of formation of water will be the same as the rate of consumption of hydrogen.

Step 5: Therefore, the rate of consumption of oxygen is 0.48 mol/s divided by 2 and the rate of formation of water is 0.48 mol/s.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass and the mole concept, allowing us to calculate the amounts of substances consumed and produced in a reaction. In this case, the balanced equation shows that two moles of hydrogen react with one mole of oxygen to produce two moles of water, which is essential for determining the rates of consumption and formation.

Mole Ratio

The mole ratio is derived from the coefficients of a balanced chemical equation and indicates the proportion of moles of one substance to another. In the combustion of hydrogen, the mole ratio between hydrogen, oxygen, and water is 2:1:2. This ratio is crucial for calculating how much oxygen is consumed and how much water is produced based on the rate of hydrogen consumption.

Reaction Rates

Reaction rates refer to the speed at which reactants are converted into products in a chemical reaction. They can be expressed in terms of the change in concentration of a reactant or product over time. In this scenario, knowing the rate of hydrogen consumption allows us to use stoichiometry and mole ratios to find the corresponding rates of oxygen consumption and water vapor formation.

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Textbook Question

For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product: (c) N21g2 + 3 H21g2¡2 NH31g2

Textbook Question

For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product:

(d) C₂H₅NH₂(g) → C₂H₄(g) + NH₃(g)

Textbook Question

For each of the following gas-phase reactions, write the rate expression in terms of the appearance of each product and disappearance of each reactant:

(a) 2 H₂O(g) → 2 H₂(g) + O₂(g)

(b) 2 SO₂(g) + O₂(g) → 2 SO₃(g)

(d) N₂(g) + 2 H₂(g) → N₂H₄(g)

Textbook Question

(b) The reaction 2 NO1g2 + Cl21g2¡2 NOCl1g2 is carried out in a closed vessel. If the partial pressure of NO is decreasing at the rate of 56 torr/min, what is the rate of change of the total pressure of the vessel?

Textbook Question

A reaction A + B → C obeys the following rate law: Rate = k[B]². (a) If [A] is doubled, how will the rate change? Will the rate constant change?