Equilibrium Reactant Concentration of First Order Opposed by First Order Reaction at given Time t Calculator

Formula Used:

\[ x_{eq} = \frac{x}{1 - e^{-(k_f + k_b) \cdot t}} \]

Concentration of Product at Time t:

mol/m³

Forward Reaction Rate Constant (k_f):

s⁻¹

Backward Reaction Rate Constant (k_b):

s⁻¹

Time (t):

Concentration of Reactant at Equilibrium (x_eq): mol/m³

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1. What is Equilibrium Reactant Concentration?

Definition: This calculator determines the equilibrium concentration of reactant in a first-order reversible reaction at a given time.

Purpose: It helps chemists and chemical engineers analyze reaction kinetics and predict equilibrium conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ x_{eq} = \frac{x}{1 - e^{-(k_f + k_b) \cdot t}} \]

Where:

\( x_{eq} \) — Equilibrium reactant concentration (mol/m³)
\( x \) — Product concentration at time t (mol/m³)
\( k_f \) — Forward reaction rate constant (s⁻¹)
\( k_b \) — Backward reaction rate constant (s⁻¹)
\( t \) — Reaction time (seconds)

Explanation: The formula accounts for both forward and backward reaction rates to determine the equilibrium state.

3. Importance of Equilibrium Calculation

Details: Understanding equilibrium concentrations is crucial for reaction optimization, process design, and predicting reaction yields.

4. Using the Calculator

Tips: Enter the product concentration, both rate constants, and reaction time. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What if my reaction hasn't reached equilibrium?
A: The calculator works for any time t, showing what the equilibrium concentration would be based on current conditions.

Q2: How do I determine the rate constants?
A: Rate constants are typically determined experimentally through kinetic studies.

Q3: Can this be used for higher-order reactions?
A: No, this formula is specific for first-order opposed by first-order reactions.

Q4: What units should I use?
A: Use consistent units: mol/m³ for concentrations, s⁻¹ for rate constants, and seconds for time.

Q5: Why does the denominator approach zero at long times?
A: As t → ∞, the exponential term → 0, and the equation simplifies to x_eq = x.