Ideal Gas Law Calculator PV = nRT

Ideal Gas Law Calculator – How It Works, Formulas, and Examples

The Ideal Gas Law Calculator helps you find one variable (Pressure $P$, Volume $V$, Moles of Gas $n$, or Temperature $T$) when the other three variables are known. It uses the ideal gas law equation:

$$PV = nRT$$

where:

• $P$ = Pressure
• $V$ = Volume
• $n$ = Moles of gas
• $R$ = Ideal Gas Constant (8.314 J/(mol·K))
• $T$ = Temperature (in Kelvin)

This calculator provides the flexibility to choose different units for pressure, volume, and temperature and allows the user to select the units in which the answer should be presented.

Using the Calculator:

1. Choose the Calculation Type Select which variable you wish to calculate from the dropdown:

   • Pressure (P) – Given volume $V$, moles of gas $n$, and temperature $T$.
   • Volume (V) – Given pressure $P$, moles of gas $n$, and temperature $T$.
   • Moles (n) – Given pressure $P$, volume $V$, and temperature $T$.
   • Temperature (T) – Given pressure $P$, volume $V$, and moles of gas $n$.

2. Input the Known Variables Enter the known values for the selected variables. Each field corresponds to one of the variables in the ideal gas equation. You must input values for the three variables that are not being calculated.

3. Select Units for Each Variable Select the appropriate units for:

   • Pressure (Pa, atm, mmHg, etc.)
   • Volume (m³, cm³, L, etc.)
   • Temperature (K, °C, °F, °R)

   The calculator will handle the necessary conversions to ensure accurate calculations.

4. Choose Units for the Answer Select the desired units in which the result should be presented (Pa for pressure, m³ for volume, K for temperature, and mol for moles).

5. Click ‘Calculate’ Press the “Calculate” button to find the unknown variable. The answer will be displayed in the selected units.

6. Click ‘Clear’ to Reset Press the “Clear” button to reset the form for a new calculation.

Formulas and Examples:

1. Calculate Pressure $P$ Formula:

   $$P = \frac{nRT}{V}$$

   Example: Find the pressure when $n = 2 \, \text{mol}$, $V = 10 \, \text{m}^3$, $T = 300 \, \text{K}$.

   $$P=\frac{(2\text{mol})\cdot (8.314\text{J/(mol·}\text{<br>}\text{K)})\cdot (300\text{K})}{10{\text{m}}^3}=498.84\text{Pa}$$

2. Calculate Volume $V$ Formula:

   $$V = \frac{nRT}{P}$$

   Example: Find the volume when $n = 1 \, \text{mol}$, $P = 101325 \, \text{Pa}$, $T = 273 \, \text{K}$.

   $$V=\frac{(1\text{mol})\cdot (8.314\text{J/(mol·}\text{<br>}\text{K)})\cdot (273\text{K})}{101325\text{Pa}}=0.0224{\text{m}}^3$$

3. Calculate Moles $n$ Formula:

   $$n = \frac{PV}{RT}$$

   Example: Find the number of moles when $P = 101325 \, \text{Pa}$, $V = 22.4 \, \text{L}$, $T = 273 \, \text{K}$. (Convert volume to $\text{m}^3$: 22.4 L = 0.0224 $\text{m}^3$)

   $$n = \frac{(101325 \, \text{Pa}) \cdot (0.0224 \, \text{m}^3)}{(8.314 \, \text{J/(mol·K)}) \cdot (273 \, \text{K})} = 1 \, \text{mol}$$

4. Calculate Temperature $T$ Formula:

   $$T = \frac{PV}{nR}$$

   Example: Find the temperature when $P = 202650 \, \text{Pa}$, $V = 0.0224 \, \text{m}^3$, $n = 1 \, \text{mol}$.

   $$T = \frac{(202650 \, \text{Pa}) \cdot (0.0224 \, \text{m}^3)}{(1 \, \text{mol}) \cdot (8.314 \, \text{J/(mol·K)})} = 546 \, \text{K}$$

Quick Tips:

• Ensure all input units are correctly selected.
• Use the conversion features provided by the calculator to get accurate results in your desired units.
• The calculator uses the universal gas constant $R = 8.314 \, \text{J/(mol·K)}$.