How to Calculate Rate of Disappearance from Rate of Formation

Rate of Disappearance Calculator

aA → bB

Calculate how fast Reactant A disappears based on how fast Product B forms.

Please enter valid positive numbers for all fields. Coefficients cannot be zero.

In chemical kinetics, the rate at which reactants are consumed (disappearance) is directly linked to the rate at which products are generated (formation) through the balanced chemical equation. Understanding this relationship is fundamental for solving stoichiometry problems in chemistry, specifically determining unknown rates based on observed data.

The Stoichiometric Relationship

For a general chemical reaction represented by the equation:

aA + bB → cC + dD

Where:

• A, B are reactants.
• C, D are products.
• a, b, c, d are the stoichiometric coefficients (the numbers in front of the chemical formulas).

According to the general rate law definition, the rate of reaction (r) relates the changes in concentration of all species as follows:

Rate = –¹⁄_a Δ[A]/Δt = +¹⁄_c Δ[C]/Δt

Note that the rate of disappearance is mathematically negative (because concentration decreases), but we often speak of the "rate" as a positive magnitude representing speed.

Formula: Calculating Rate of Disappearance

To find the rate of disappearance of a reactant (A) given the rate of formation of a product (C), you simply multiply the formation rate by the molar ratio of the reactant to the product.

Rate of Disappearance of A = (a / c) × Rate of Formation of C

Where:

• a = Coefficient of the Reactant (disappearing)
• c = Coefficient of the Product (forming)

Step-by-Step Calculation Example

Consider the Haber process for the synthesis of ammonia:

N₂ + 3H₂ → 2NH₃

Problem: If Ammonia (NH₃) is being formed at a rate of 0.50 M/s, what is the rate of disappearance of Hydrogen (H₂)?

1. Identify Coefficients:
   • Reactant (H₂) coefficient (a) = 3
   • Product (NH₃) coefficient (b) = 2
2. Identify Known Rate: Rate of formation of NH₃ = 0.50 M/s.
3. Apply Formula:
   Rate H₂ = (3 / 2) × 0.50 M/s
   Rate H₂ = 1.5 × 0.50
   Rate H₂ = 0.75 M/s

Thus, Hydrogen is disappearing at a rate of 0.75 M/s.

Why are Stoichiometric Coefficients Important?

The coefficients tell you the molar ratio. In the example above, for every 2 moles of Ammonia produced, 3 moles of Hydrogen must be consumed. Therefore, the Hydrogen must be consumed faster (1.5 times faster) than the Ammonia is produced to sustain the reaction balance.

Common Units

Reaction rates are typically expressed in:

• M/s (Molarity per second or mol/L/s)
• mol/min (Moles per minute)
• Pa/s (Pascals per second for gases)

Our calculator works with any unit as long as you use the same unit for both disappearance and formation rates.