Ideal Gas Law Calculator Online

 The ideal gas law calculator is a tool that determines unknown properties of an ideal gas when three of the variables in the equation 

$PV=nRT$ are known.

Understanding Ideal Gases

An ideal gas is a theoretical concept, representing a collection of particles that move randomly and interact through perfectly elastic collisions. This model simplifies the behavior of gases under various conditions, even though no real gas behaves perfectly as an ideal gas.

Ideal Gas Law Equation

The fundamental equation for the ideal gas law is:$PV=nRT$This equation allows for the calculation of unknown values such as pressure, volume, temperature, or the number of moles of a gas.

Calculating Variables

Here’s how to rearrange the ideal gas law to solve for different variables:

• Pressure (P):$P=\frac{nRT}{V}$
• Volume (V):$V=\frac{nRT}{P}$
• Number of Moles (n):$n=\frac{PV}{RT}$
• Temperature (T):$T=\frac{PV}{nR}$

Where:

• $n$ = number of moles
• $R$ = ideal gas constant (8.3145 J/mol·K)
• $T$ = temperature in Kelvin
• $P$ = pressure in Pascals
• $V$ = volume

The Gas Constant (R)

The gas constant, denoted as $R$, is a crucial physical constant used in various equations across physical sciences. It combines constants from Boyle’s law, Charles's law, Avogadro's law, and Gay-Lussac's law. The value of $R$ is typically 8.3144626 J/(mol·K).

Laws Incorporated in the Ideal Gas Equation

The ideal gas law integrates several fundamental gas laws:

1. Boyle's Law: At constant temperature and quantity of gas, pressure and volume are inversely related.
   $P_1{V}_1=P_2{V}_2$
2. Charles's Law: At constant pressure and quantity, volume is directly proportional to temperature.
   $\frac{V_1}{T_1}=\frac{V_2}{T_2}$
3. Gay-Lussac's Law: At constant volume and quantity, pressure is directly proportional to temperature.
   $\frac{P_1}{T_1}=\frac{P_2}{T_2}$
4. Avogadro’s Law: At constant temperature and pressure, volume is directly proportional to the number of moles.
   $\frac{V_1}{n_1}=\frac{V_2}{n_2}$

Steps to Calculate Using the Ideal Gas Law

To effectively use the ideal gas law:

1. Identify known values for pressure (P), volume (V), temperature (T), and number of moles (n).
2. Convert units if necessary.
3. Substitute the known values into the ideal gas formula.

Example Calculations

Case 1: Finding VolumeGiven:

• Pressure = 200 kPa
• Temperature = 300 K
• Moles ($n$) = 0.250 mol

Calculate volume ($V$):
$V=\frac{nRT}{P}=\frac{0.250\times 8.314\times 300}{200000}\approx 3.12L$Case 2: Finding TemperatureGiven:

• Pressure = 153 kPa
• Volume = 250 ml (converted to 0.250 L)
• Moles ($n$) = 0.50 mol

Calculate temperature ($T$):
$T=\frac{PV}{nR}=\frac{153000\times 0.250}{0.50\times 8.314}\approx 9.2K$

Frequently Asked Questions

When is the Ideal Gas Law Applicable?

The ideal gas law is most applicable under conditions of:

• High temperatures
• Low pressures
• Sufficient volumes
• Non-reacting gases