Question

(a) Consider the combustion of \(\mathrm{H}_{2}(g): 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)\) \(\longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) .\) If hydrogen is buming at the rate of \(0.85 \mathrm{~mol} / \mathrm{s}\), what is the rate of consumption of oxygen? What is the rate of formation of water vapor? (b) The reaction \(2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{NOCl}(g)\) is carried out in a closed vessel. If the partial pressure of \(\mathrm{NO}\) is decreasing at the rate of 23 torr/min, what is the rate of change of the total pressure of the vessel?

Short answer

The short answer based on the step-by-step solution is: For part (a): - The rate of consumption of oxygen gas is 0.425 mol/s. - The rate of formation of water vapor is 0.85 mol/s. For part (b): - The rate of change of the total pressure of the vessel is 0 torr/min.

Step-by-step solution

Write down the balanced chemical equation

The balanced chemical equation is given as: \(2 H_2(g) + O_2(g) \longrightarrow 2 H_2O(g)\)

Rate of consumption of oxygen

Recall that for every 2 moles of hydrogen consumed, 1 mole of oxygen is consumed. Use the given rate of hydrogen consumption to find the rate of oxygen consumption: Rate of oxygen consumption = (Rate of hydrogen consumption) / 2 Rate of oxygen consumption = (0.85 mol/s) / 2 = 0.425 mol/s

Rate of formation of water vapor

Since for every 2 moles of hydrogen consumed, 2 moles of water vapor are formed, the rate of water vapor formation is equal to the rate of hydrogen consumption: Rate of water vapor formation = Rate of hydrogen consumption = 0.85 mol/s For part (a): - The rate of consumption of oxygen gas is 0.425 mol/s. - The rate of formation of water vapor is 0.85 mol/s. (b)

Write down the balanced chemical equation

The balanced chemical equation is given as: \(2 NO(g) + Cl_2(g) \longrightarrow 2 NOCl(g)\)

Determine the decrease in the total number of moles due to the reaction

From the balanced equation, we can see that for every 2 moles of NO consumed, 1 mole of Cl_2 is consumed, and 2 moles of NOCl are formed. Therefore, there is no overall change in the total number of moles as a result of the reaction.

Determine the rate of change of the total pressure

Since there is no overall change in the total number of moles of gas as a result of the reaction, it follows that the rate of change of the total pressure of the vessel is zero: Rate of change of total pressure = 0 torr/min For part (b): - The rate of change of the total pressure of the vessel is 0 torr/min.

Key concepts

Rate of Reaction

Understanding how quickly a chemical reaction proceeds is crucial in both academic and industrial settings. The rate of a reaction, often expressed in moles per second (mol/s), determines how much reactant is consumed or how much product is formed over a specific time period.

In our combustion example, we can observe the rate at which hydrogen gas (H₂) burns to form water vapor (H₂O). By determining that 0.85 mol of H₂ reacts per second, we have directly measured the reaction rate for H₂. Applying stoichiometry, we can calculate the associated rates for consumption of oxygen (O₂) and the formation of water vapor, showcasing how interconnected these rates are within a balanced chemical equation.

Stoichiometry

Stoichiometry is like the recipe for a chemical reaction. It tells you exactly how much of each ingredient (reactant) is needed to make your desired product. In the example of hydrogen combustion, the balanced equation reveals a stoichiometric ratio of 2:1:2 between hydrogen, oxygen, and water vapor.

To find out how much oxygen is used up when hydrogen burns, we use stoichiometry to relate the rates. Since the equation shows that one mole of oxygen is needed for every two moles of hydrogen, the rate of oxygen consumption is half the rate of hydrogen consumption. This kind of calculation is essential for predicting how much of each reactant is needed and how much product will be formed in a given period.

Gas Laws

The behavior of gases during a reaction is often explained by gas laws. These laws relate the volume, temperature, pressure, and number of moles of a gas. An important concept linked with the gas laws is that a change in the number of moles of gas, at constant temperature and volume, will result in a change in pressure—the more moles of gas, the higher the pressure.

In the case of the reaction involving nitrogen monoxide (NO) and chlorine (Cl₂), despite the ongoing reaction, there's no change in the total number of gas molecules because for every two NO molecules consumed, two NOCl molecules are formed. Based on gas laws, this equilibrium leads to no change in the total pressure inside the closed vessel as long as the temperature remains constant.

Balanced Chemical Equations

A chemical equation is a representation of a chemical reaction where the reactants and products are expressed in terms of their molecular formulas. A balanced chemical equation has equal numbers of each type of atom on both the reactant and product sides, abiding by the law of conservation of mass.

In practical terms, balancing equations allows us to quantify the relationship between reactants and products. This concept is fundamental when determining reaction rates, as seen in the examples provided. A balanced equation ensures that the stoichiometry is correct, so when we calculate the rate of oxygen consumption or the rate of water vapor formation, our calculations reflect the actual physical process.