Stoichiometric Rate Calculations: Videos & Practice Problems

To calculate the rate of formation of one compound from the known rate of decomposition of another within a balanced chemical equation, perform a rate-to-rate comparison using stoichiometric coefficients. For instance, if the decomposition rate of H₂ is 1.54 mol/L per minute, the formation rate of nitrogen gas can be determined by setting up a ratio based on the stoichiometric coefficients. As H₂ decomposes twice as fast as N₂ forms (a 2:1 ratio), the formation rate of N₂ would be half that of H₂, resulting in 0.770 mol/L per minute. This method is an application of stoichiometry principles to reaction rates, allowing one to find the rate of any compound provided the rate of another in the same reaction.

Stoichiometric Rate Calculations

Stoichiometric rate calculations are essential in understanding the relationship between the rates of different compounds in a chemical reaction. When the rate of one compound is known, the rate of another can be determined through a rate-to-rate comparison based on the stoichiometric coefficients from the balanced chemical equation.

For instance, consider a scenario where the rate of decomposition of hydrogen gas (H₂) is given as 1.54 molarity per minute. To find the rate of formation of nitrogen gas (N₂) at the same time, we can follow a systematic approach.

First, since the rate of H₂ is provided, we can directly use this information. The next step involves performing a rate-to-rate comparison using the stoichiometric coefficients from the balanced equation. In this case, if the balanced equation indicates that 2 moles of H₂ produce 1 mole of N₂, we can set up the comparison as follows:

Given:

Rate of H₂ = 1.54 M/min

Stoichiometric coefficients: 2 for H₂ and 1 for N₂

Using the coefficients, we can express the relationship:

Rate of N₂ = Rate of H₂ × (1/2)

Substituting the known rate:

Rate of N₂ = 1.54 M/min × (1/2) = 0.770 M/min

Thus, the rate of formation of nitrogen gas (N₂) is 0.770 molarity per minute. This method highlights the importance of stoichiometric coefficients in converting rates, allowing for the determination of the rate of any compound in a balanced equation when the rate of another compound is known.

The formation of alumina, Al₂O₃, can be illustrated by the reaction below:
4 Al (s) + 3 O₂ (g) → 2 Al₂O₃ (s)
At 750 K it takes 267 seconds for the initial concentration of Al₂O₃ to increase from 6.18 x 10^-5 M to 5.11 x 10^-4 M. What is the average rate of Al?

• A. 8.41 x 10^-7 M/s
• B. 1.68 x 10^-6 M/s
• C. 3.36 x 10^-6 M/s
• D. 4.21 x 10^-7 M/s

Answer: (C)

Here’s what students ask on this topic:

How do you perform stoichiometric rate calculations in a chemical reaction?

To perform stoichiometric rate calculations, you need to know the rate of one compound in a balanced chemical equation. Using this known rate, you can calculate the rate of another compound by performing a rate-to-rate comparison using stoichiometric coefficients. For example, if the decomposition rate of H₂ is 1.54 mol/L per minute, and the balanced equation shows a 2:1 ratio between H₂ and N₂, the formation rate of N₂ would be half that of H₂, resulting in 0.770 mol/L per minute. This method applies stoichiometry principles to reaction rates, allowing you to find the rate of any compound given the rate of another in the same reaction.

What is the significance of stoichiometric coefficients in rate calculations?

Stoichiometric coefficients are crucial in rate calculations because they indicate the relative amounts of reactants and products involved in a chemical reaction. When performing stoichiometric rate calculations, these coefficients help establish the ratio between the rates of different compounds. For instance, in the reaction 2H₂ → N₂, the coefficient 2 for H₂ and 1 for N₂ means that H₂ decomposes twice as fast as N₂ forms. This ratio allows you to convert the known rate of one compound to the rate of another, ensuring accurate calculations based on the balanced equation.

Can you explain the steps to calculate the rate of formation of a product from the rate of decomposition of a reactant?

To calculate the rate of formation of a product from the rate of decomposition of a reactant, follow these steps: 1) Identify the known rate of the reactant. 2) Write the balanced chemical equation for the reaction. 3) Determine the stoichiometric coefficients for the reactant and product. 4) Set up a rate-to-rate comparison using these coefficients. For example, if the decomposition rate of H₂ is 1.54 mol/L per minute and the balanced equation is 2H₂ → N₂, the formation rate of N₂ is calculated as (1.54 mol/L per minute) × (1 mol N₂ / 2 mol H₂) = 0.770 mol/L per minute.

What is the difference between mole-to-mole and rate-to-rate comparisons in stoichiometry?

Mole-to-mole comparisons in stoichiometry involve converting the amount of one substance to another using the stoichiometric coefficients from a balanced chemical equation. Rate-to-rate comparisons, on the other hand, involve converting the rate of one substance to the rate of another using the same stoichiometric coefficients. While mole-to-mole comparisons focus on the quantities of substances, rate-to-rate comparisons focus on the rates at which these substances react or form. Both methods use the stoichiometric coefficients to ensure accurate conversions based on the balanced equation.

How do you determine the rate of a compound if the rate of another compound is not given directly?

If the rate of a compound is not given directly, you can determine it using other provided information. First, identify any given data related to the reaction, such as concentrations, time, or other rates. Use this information to calculate the missing rate. For example, if you know the initial and final concentrations of a reactant and the time taken for the reaction, you can calculate the rate of the reactant's decomposition. Once you have this rate, you can perform a rate-to-rate comparison using stoichiometric coefficients to find the rate of another compound in the reaction.