Volume of Monolayer Gas by BET Equation Calculator

BET Equation Formula:

\[ V_{mono} = \frac{(P_v - \frac{P_v}{P_0}) \times (1 + (C \times \frac{P_v}{P_0})) - (\frac{P_v}{P_0} \times V_{total})}{C \times \frac{P_v}{P_0}} \]

Vapour Pressure (P_v):

Saturated Vapor Pressure (P₀):

Adsorbent Constant (C):

Total Equilibrium Volume (V_total):

m³

Monolayer Volume (V_mono):

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1. What is Volume of Monolayer Gas by BET Equation?

Definition: This calculator determines the volume of gas required to form a monolayer on the surface of an adsorbent using the Brunauer-Emmett-Teller (BET) equation.

Purpose: It's essential for surface area measurements in materials science, particularly for porous materials and catalysts.

2. How Does the BET Equation Work?

The calculator uses the BET equation:

\[ V_{mono} = \frac{(P_v - \frac{P_v}{P_0}) \times (1 + (C \times \frac{P_v}{P_0})) - (\frac{P_v}{P_0} \times V_{total})}{C \times \frac{P_v}{P_0}} \]

Where:

\( V_{mono} \) — Monolayer volume of gas (m³)
\( P_v \) — Vapour pressure (Pa)
\( P_0 \) — Saturated vapor pressure (Pa)
\( C \) — Adsorbent constant (dimensionless)
\( V_{total} \) — Total equilibrium volume of gas (m³)

Explanation: The equation accounts for multilayer adsorption and provides the volume needed for complete monolayer coverage.

3. Importance of Monolayer Volume Calculation

Details: Accurate monolayer volume determination is crucial for calculating specific surface area, which affects material properties like reactivity and adsorption capacity.

4. Using the Calculator

Tips: Enter all required parameters in consistent units. Vapour pressure and saturated pressure must be in the same units (Pa in this case).

5. Frequently Asked Questions (FAQ)

Q1: What is the physical meaning of the adsorbent constant C?
A: The C constant relates to the heat of adsorption of the first layer compared to the heat of liquefaction.

Q2: What's a typical range for C values?
A: C values typically range from 50-200 for most adsorbents, with higher values indicating stronger adsorbate-adsorbent interactions.

Q3: How do I determine P₀?
A: P₀ is the saturation vapor pressure of the adsorbate at the measurement temperature, available from thermodynamic tables.

Q4: What are common gases used in BET measurements?
A: Nitrogen at 77K is most common, but argon and krypton are also used depending on the material.

Q5: What's the relationship between V_mono and surface area?
A: Surface area = (V_mono × N × σ) / (V_m), where N is Avogadro's number, σ is adsorbate cross-sectional area, and V_m is molar volume.