Molar Flow Rate to Volumetric Flow Rate Calculator

Molar Flow Rate to Volumetric Flow Rate Calculator (Ideal Gas)

Assumes ideal gas behavior.

mol/s mol/min kmol/h

function calculateVolumetricFlow() { var molarFlowInput = document.getElementById('molarFlowRate').value; var molarFlowUnit = document.getElementById('molarFlowUnit').value; var tempCelsius = document.getElementById('temperature').value; var pressureAtm = document.getElementById('pressure').value; var resultDiv = document.getElementById('result'); var resultM3sSpan = document.getElementById('resultM3s'); var resultLminSpan = document.getElementById('resultLmin'); // Validate inputs if (molarFlowInput === "" || tempCelsius === "" || pressureAtm === "") { alert("Please fill in all fields correctly."); return; } var n_dot = parseFloat(molarFlowInput); var T_c = parseFloat(tempCelsius); var P_atm = parseFloat(pressureAtm); if (isNaN(n_dot) || isNaN(T_c) || isNaN(P_atm) || P_atm <= 0 || n_dot < 0) { alert("Please enter valid numeric values. Pressure must be greater than 0 and flow rate cannot be negative."); return; } // Constants var R = 8.314462618; // Universal gas constant in J/(mol·K) or (m³·Pa)/(mol·K) var atmToPa = 101325; // Conversion factor from atm to Pascals // Convert inputs to standard SI units (mol/s, Kelvin, Pascals) var n_dot_mol_s; if (molarFlowUnit === "mol_s") { n_dot_mol_s = n_dot; } else if (molarFlowUnit === "mol_min") { n_dot_mol_s = n_dot / 60; } else if (molarFlowUnit === "kmol_h") { n_dot_mol_s = (n_dot * 1000) / 3600; } var T_k = T_c + 273.15; // Temperature in Kelvin var P_pa = P_atm * atmToPa; // Pressure in Pascals // Calculate Volumetric Flow Rate (V_dot) in m³/s using V_dot = (n_dot * R * T) / P var V_dot_m3s = (n_dot_mol_s * R * T_k) / P_pa; // Convert result to L/min // 1 m³ = 1000 L, 1 s = 1/60 min var V_dot_Lmin = V_dot_m3s * 1000 * 60; // Display results resultM3sSpan.textContent = V_dot_m3s.toExponential(4); resultLminSpan.textContent = V_dot_Lmin.toFixed(2); resultDiv.style.display = "block"; }

Understanding Molar to Volumetric Flow Rate Conversion

In chemical engineering and process industries, it's common to need to convert between molar flow rate and volumetric flow rate. Molar flow rate measures the number of moles of a substance passing a point per unit of time, while volumetric flow rate measures the volume of that substance passing per unit of time.

For gases, this relationship is heavily dependent on temperature and pressure. This calculator uses the **Ideal Gas Law** to perform the conversion, which is a good approximation for many common gases under standard conditions.

The Formula

The Ideal Gas Law is usually written as PV = nRT. By dividing by time (t), we get the relationship for flow rates:

P × V̇ = ṅ × R × T

Where:

• P = Absolute Pressure (in Pascals, Pa)
• V̇ = Volumetric Flow Rate (in cubic meters per second, m³/s)
• ṅ = Molar Flow Rate (in moles per second, mol/s)
• R = Universal Gas Constant (approximately 8.314 J/(mol·K))
• T = Absolute Temperature (in Kelvin, K)

To find the volumetric flow rate, we rearrange the formula:

V̇ = (ṅ × R × T) / P

Example Calculation

Let's say you have a nitrogen gas stream with a molar flow rate of 50 mol/min. The process temperature is 25 °C and the pressure is 1.5 atm.

1. Convert inputs to SI units:
   • ṅ = 50 mol/min ÷ 60 s/min ≈ 0.8333 mol/s
   • T = 25 °C + 273.15 = 298.15 K
   • P = 1.5 atm × 101325 Pa/atm = 151987.5 Pa
2. Apply the formula:
   • V̇ = (0.8333 × 8.314 × 298.15) / 151987.5
   • V̇ ≈ 2065.5 / 151987.5 ≈ 0.01359 m³/s
3. Convert to a more convenient unit like L/min:
   • 0.01359 m³/s × 1000 L/m³ × 60 s/min ≈ 815.4 L/min

This calculator automates these steps, allowing you to quickly determine the volumetric flow requirement for pumps, compressors, or piping sizing based on your process's molar balance.