1. What is Instantaneous Rate?

The instantaneous rate of reaction is the rate at a particular moment in time, represented by the slope of the tangent to the concentration-time curve at that point. It's mathematically defined as the derivative of concentration with respect to time.

2. How Does the Calculator Work?

The calculator uses the instantaneous rate formula:

Where:

• \( [A] \) — Concentration of reactant A (mol/L)
• \( [P] \) — Concentration of product P (mol/L)
• \( t \) — Time (seconds)
• The negative sign indicates decreasing reactant concentration

Explanation: The calculator approximates the derivative using finite changes in concentration and time.

3. Importance of Instantaneous Rate

Details: Instantaneous rates are crucial for determining reaction mechanisms, calculating rate laws, and understanding reaction kinetics at specific points in time.

4. Using the Calculator

Tips: Enter the change in concentration (Δ[A] or Δ[P]) in mol/L and the corresponding time interval in seconds. Select whether you're measuring a reactant or product.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between average and instantaneous rate?
A: Average rate is over a time interval, while instantaneous rate is at a specific moment (as Δt approaches 0).

Q2: Why is the reactant rate negative?
A: By convention, reactant rates are negative because their concentrations decrease with time.

Q3: How small should Δt be for a good approximation?
A: The smaller Δt, the better the approximation of the true instantaneous rate.

Q4: Can this be used for any reaction order?
A: Yes, the instantaneous rate concept applies to all reaction orders.

Q5: How does this relate to rate laws?
A: Instantaneous rates at different concentrations are used to determine rate law exponents.