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

Now stoichiometric rate calculations happen when the rate of one compound is known and the rate of another can be calculated using a rate to rate comparison. So here in this example it says if the rate of decomposition of H₂ is 1.54 molarities per minute at a particular time, what will be the rate of formation of nitrogen gas at that same time? So they're giving us the rate of one compound and asking for the rate of another within a balanced chemical equation. This is a key giveaway that you're dealing with a stoichiometric rate calculation.

Now here step one. If the rate of change for one compound is not given, then first calculate it using information provided here. We don't have to worry about that because we're given the rate of H₂ right from the beginning. It's 1.54 molarities per minute. Now Step 2, using the rate of one compound, perform a rate to rate comparison using stoichiometric coefficients. Now this is similar to a mole to mole comparison that we've used before in stoichiometry.

Now the way we'd set it up is we have 1.54 molarity per minute and this is for H₂. And remember in stoichiometry we do a multiple comparison, but now we're doing a rate to rate comparison. So we're going to say according to our balanced chemical equation, we have two here for H₂. That two would mean 2 molarities per minute for H₂ and then for N₂. There's a one here, so that's one molarities per minute for N₂. So here our units will cancel out and look, we're going to have the rate of N₂.

So when we plug that in, we get 0.770 molarities per minute for N₂. So this would be the rate of nitrogen gas. So again it's kind of reminiscent a little bit of stoichiometry, but instead of doing a mole to mole comparison, we're doing a rate to rate comparison. So approach it in the same manner, and you'll always be able to find the rate of any compound within a balanced equation if they give you a rate of another compound within that same balanced equation.

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.