How to Calculate Molar Flow Rate of Gas

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Molar Flow Rate Calculator for Gas

Gas Molar Flow Rate Calculator

Calculate the molar flow rate ($n$) based on volumetric flow, pressure, and temperature using the Ideal Gas Law.

m³/h m³/s L/min CFM (ft³/min)
atm bar Pa psi
°C °F K

Calculation Results:

Molar Flow Rate (SI) 0.000 mol/s
Molar Flow Rate (Hourly) 0.000 kmol/h
Equation Used: n = (P × V) / (R × T)
Where R = 8.314 J/(mol·K)

How to Calculate Molar Flow Rate of Gas

Understanding the molar flow rate is essential in chemical engineering, process dynamics, and thermodynamics. Unlike volumetric flow rate, which changes based on pressure and temperature, the molar flow rate represents the actual amount of substance (number of moles) passing through a system per unit of time. This makes it a critical metric for mass balance calculations.

The Molar Flow Rate Formula

For gases, the most common way to calculate the molar flow rate is by deriving it from the Volumetric Flow Rate using the Ideal Gas Law. The formula is:

n = (P × V) / (R × T)

Where:

  • n = Molar Flow Rate (mol/s)
  • P = Absolute Pressure (Pa)
  • V = Volumetric Flow Rate (m³/s)
  • R = Universal Gas Constant (approx. 8.314 J/(mol·K))
  • T = Absolute Temperature (Kelvin)

Step-by-Step Calculation Example

Let's calculate the molar flow rate for an air compressor system with the following readings:

  • Flow Rate: 500 m³/h
  • Pressure: 2 bar (gauge pressure assumed absolute for this example)
  • Temperature: 25 °C

Step 1: Convert units to SI (Standard International) units.

  • Pressure: 2 bar × 100,000 = 200,000 Pa
  • Flow: 500 m³/h ÷ 3600 = 0.1389 m³/s
  • Temperature: 25 °C + 273.15 = 298.15 K

Step 2: Apply the Ideal Gas Law.

n = (200,000 × 0.1389) / (8.314 × 298.15)
n = 27,780 / 2,478.8
n ≈ 11.21 mol/s

Why Convert Volumetric Flow to Molar Flow?

In gas systems, volume is not a conserved quantity. If you compress gas, the volume decreases, but the amount of gas (moles) remains constant. When designing reactors, piping systems, or analyzing chemical reactions, engineers must use molar flow rates to ensure stoichiometry is respected and mass balances are accurate.

function calculateMolarFlow() { // 1. Get Input Values var volFlowInput = document.getElementById('volFlow').value; var pressureInput = document.getElementById('pressure').value; var tempInput = document.getElementById('temperature').value; var volFlowUnit = document.getElementById('volFlowUnit').value; var pressureUnit = document.getElementById('pressureUnit').value; var tempUnit = document.getElementById('tempUnit').value; var resultContainer = document.getElementById('resultContainer'); var errorMsg = document.getElementById('errorMsg'); // 2. Validation if (volFlowInput === "" || pressureInput === "" || tempInput === "") { errorMsg.style.display = 'block'; errorMsg.innerHTML = "Please fill in all fields (Flow, Pressure, and Temperature)."; resultContainer.style.display = 'none'; return; } var V = parseFloat(volFlowInput); var P = parseFloat(pressureInput); var T = parseFloat(tempInput); if (V <= 0 || P <= 0) { errorMsg.style.display = 'block'; errorMsg.innerHTML = "Flow Rate and Pressure must be positive numbers."; resultContainer.style.display = 'none'; return; } // 3. Convert all inputs to SI Units (m3/s, Pa, K) // Convert Flow to m3/s var flowSI = 0; // m3/s if (volFlowUnit === 'm3s') { flowSI = V; } else if (volFlowUnit === 'm3h') { flowSI = V / 3600; } else if (volFlowUnit === 'lmin') { flowSI = V / 1000 / 60; } else if (volFlowUnit === 'cfm') { flowSI = V * 0.000471947; } // Convert Pressure to Pa var pressureSI = 0; // Pa if (pressureUnit === 'pa') { pressureSI = P; } else if (pressureUnit === 'bar') { pressureSI = P * 100000; } else if (pressureUnit === 'atm') { pressureSI = P * 101325; } else if (pressureUnit === 'psi') { pressureSI = P * 6894.76; } // Convert Temperature to Kelvin var tempSI = 0; // K if (tempUnit === 'k') { tempSI = T; } else if (tempUnit === 'c') { tempSI = T + 273.15; } else if (tempUnit === 'f') { tempSI = (T – 32) * (5/9) + 273.15; } // Check for Absolute Zero violation if (tempSI <= 0) { errorMsg.style.display = 'block'; errorMsg.innerHTML = "Temperature cannot be at or below absolute zero (0 K)."; resultContainer.style.display = 'none'; return; } // 4. Calculate Molar Flow Rate: n = PV / RT var R = 8.314462618; // Ideal Gas Constant J/(mol·K) var molarFlowMolSec = (pressureSI * flowSI) / (R * tempSI); // Calculate other units for display // kmol/h = (mol/s * 3600) / 1000 = mol/s * 3.6 var molarFlowKmolHour = molarFlowMolSec * 3.6; // 5. Display Results errorMsg.style.display = 'none'; resultContainer.style.display = 'block'; document.getElementById('resMolSec').innerText = molarFlowMolSec.toLocaleString('en-US', { minimumFractionDigits: 3, maximumFractionDigits: 3 }); document.getElementById('resKmolHour').innerText = molarFlowKmolHour.toLocaleString('en-US', { minimumFractionDigits: 3, maximumFractionDigits: 3 }); }

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