Calculate one of the four variables (Pressure, Volume, Amount of Substance, or Temperature) when the other three are known.
Pressure (P)
Volume (V)
Amount of Substance (n)
Temperature (T)
Understanding the Ideal Gas Law
The Ideal Gas Law is a fundamental equation in thermodynamics and chemistry that describes the behavior of ideal gases. An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. While no real gas is truly ideal, the Ideal Gas Law provides a very good approximation for the behavior of many gases under a wide range of conditions, especially at low pressures and high temperatures.
The Equation:
The Ideal Gas Law is expressed mathematically as:
PV = nRT
Where:
P is the pressure of the gas (typically in Pascals (Pa) or atmospheres (atm)).
V is the volume of the gas (typically in cubic meters (m³) or liters (L)).
n is the amount of substance of the gas (in moles (mol)).
R is the ideal gas constant. Its value depends on the units used for pressure, volume, and temperature. Common values include:
8.314 J/(mol·K) – when P is in Pascals, V is in cubic meters.
0.08206 L·atm/(mol·K) – when P is in atmospheres, V is in liters.
T is the absolute temperature of the gas (in Kelvin (K)). Note: Temperatures must always be in Kelvin for gas law calculations. To convert Celsius to Kelvin, add 273.15 (K = °C + 273.15).
How the Calculator Works:
This calculator rearranges the Ideal Gas Law equation (PV = nRT) to solve for any of the four primary variables (P, V, n, T) when the other three are provided. The gas constant 'R' is assumed to be 8.314 J/(mol·K), meaning the input values should be in Pascals (Pa) for pressure, cubic meters (m³) for volume, moles (mol) for the amount of substance, and Kelvin (K) for temperature.
If calculating Pressure (P): P = nRT / V
If calculating Volume (V): V = nRT / P
If calculating Amount of Substance (n): n = PV / RT
If calculating Temperature (T): T = PV / nR
Use Cases:
The Ideal Gas Law and this calculator are useful in various scientific and engineering fields:
Chemistry: Determining the conditions of reactions, stoichiometry involving gases, and gas properties.
Physics: Understanding the behavior of gases in engines, balloons, and atmospheric science.
Engineering: Designing systems that involve gas handling, such as HVAC systems, chemical processing plants, and industrial pipelines.
Education: Helping students learn and apply fundamental gas laws.
Important Considerations:
Units: Ensure all input values use consistent units (Pa for pressure, m³ for volume, mol for amount, K for temperature) as the calculator uses R = 8.314 J/(mol·K). If your initial values are in different units (e.g., atm, L, °C), you must convert them before using the calculator.
Ideal vs. Real Gases: The Ideal Gas Law is an approximation. Real gases deviate from ideal behavior, particularly at high pressures and low temperatures, where intermolecular forces and molecular volume become significant. For such conditions, more complex equations of state (like the Van der Waals equation) may be necessary.
Absolute Temperature: Always use Kelvin for temperature. Celsius or Fahrenheit must be converted.
var R = 8.314; // Ideal gas constant in J/(mol·K) – assumes P in Pa, V in m³, n in mol, T in K
function calculateGasLaw() {
var pressureInput = document.getElementById("pressure");
var volumeInput = document.getElementById("volume");
var amountInput = document.getElementById("amount");
var temperatureInput = document.getElementById("temperature");
var unknownSelect = document.getElementById("unknown");
var resultDiv = document.getElementById("result");
var p = parseFloat(pressureInput.value);
var v = parseFloat(volumeInput.value);
var n = parseFloat(amountInput.value);
var t = parseFloat(temperatureInput.value);
var unknown = unknownSelect.value;
var calculatedValue = NaN;
var resultUnit = "";
var resultLabel = "";
// Input validation: Ensure provided values are valid numbers and positive where applicable
var validInputs = {};
if (!isNaN(p) && p > 0) validInputs.p = true;
if (!isNaN(v) && v > 0) validInputs.v = true;
if (!isNaN(n) && n > 0) validInputs.n = true;
if (!isNaN(t) && t > 0) validInputs.t = true;
// Check if enough inputs are provided and valid for the selected unknown
var providedCount = 0;
if (validInputs.p) providedCount++;
if (validInputs.v) providedCount++;
if (validInputs.n) providedCount++;
if (validInputs.t) providedCount++;
if (providedCount < 3) {
resultDiv.innerText = "Please provide at least three valid inputs.";
return;
}
try {
if (unknown === "pressure") {
resultLabel = "Calculated Pressure (P): ";
resultUnit = " Pa";
if (validInputs.n && validInputs.r && validInputs.t && validInputs.v) {
calculatedValue = (n * R * t) / v;
} else {
resultDiv.innerText = "Invalid input values for pressure calculation.";
return;
}
} else if (unknown === "volume") {
resultLabel = "Calculated Volume (V): ";
resultUnit = " m³";
if (validInputs.p && validInputs.n && validInputs.r && validInputs.t) {
calculatedValue = (n * R * t) / p;
} else {
resultDiv.innerText = "Invalid input values for volume calculation.";
return;
}
} else if (unknown === "amount") {
resultLabel = "Calculated Amount of Substance (n): ";
resultUnit = " mol";
if (validInputs.p && validInputs.v && validInputs.r && validInputs.t) {
calculatedValue = (p * v) / (R * t);
} else {
resultDiv.innerText = "Invalid input values for amount calculation.";
return;
}
} else if (unknown === "temperature") {
resultLabel = "Calculated Temperature (T): ";
resultUnit = " K";
if (validInputs.p && validInputs.v && validInputs.n && validInputs.r) {
calculatedValue = (p * v) / (n * R);
} else {
resultDiv.innerText = "Invalid input values for temperature calculation.";
return;
}
}
if (!isNaN(calculatedValue)) {
resultDiv.innerText = resultLabel + calculatedValue.toFixed(5) + resultUnit;
} else {
resultDiv.innerText = "Calculation resulted in an invalid number. Check inputs.";
}
} catch (e) {
resultDiv.innerText = "An error occurred during calculation.";
console.error("Calculation Error: ", e);
}
}