Partial Pressure Calculator

Partial Pressure Calculator 

Use this Partial Pressure Calculator to determine the partial pressure of each gas in a mixture based on the moles of gasses, temperature, and volume. Also known as Dalton’s law calculator, this tool provides results in an instant.

What is partial pressure?

Partial pressure is the pressure exerted by a single gas in a mixture of gasses. It is directly proportional to the moles of the specific gas and the total pressure of the gas mixture.

The concept of partial pressure can be traced back to the work of the French chemist and physicist Joseph Louis Gay-Lussac (1778-1850) and the English scientist John Dalton (1766-1844). 

The formula of partial pressure:

The partial pressure of a gas (Pi) can be calculated using the ideal gas law:

Pi = (ni * R * T) / V

Where:

Pi: Partial pressure of the gas i (atm)

ni: Moles of the gas i (mol)

R: Ideal gas constant (0.0821 Latm/molK)

T: Temperature (K)

V: Volume (L)

Deviation of the formula:

The understanding of partial pressure as a component of the total pressure in a gas mixture is often attributed to Dalton's law, which was formulated by John Dalton in 1801.

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of gasses is equal to the sum of the partial pressures of the individual gasses in the mixture. Mathematically, it can be expressed as

Ptotal = P1 + P2 + ... + Pn

where Ptotal is the total pressure and Pi is the partial pressure of the i-th gas.

The formula for partial pressure is derived from the ideal gas law, which provides a relationship between the pressure (P), volume (V), temperature (T), and moles (n) of an ideal gas. It is given by:

PV = nRT

where R is the ideal gas constant (0.0821 Latm/molK).

To calculate the partial pressure of a gas in a mixture, we apply the ideal gas law to the individual gas. Considering the gas mixture as a whole, the total pressure (Ptotal ) can be expressed as

Ptotal * V = (n1+ n2+ ... + nn) * R * T

Now, for each individual gas, the ideal gas law is given by:

Pi * V = ni * R * T

Rearranging the equation to find the partial pressure (Pi) of the individual gas, we get:

Pi = (ni * R * T) / V

This formula allows us to calculate the partial pressure of a gas in a mixture using the number of moles of the gas, temperature, and volume.

How to calculate the partial pressure of a gas?

Besides using the partial pressure calculator for a quick answer, you can use the manual method as given ahead.

1. Convert the temperature to Kelvin (K) if it is given in Celsius or Fahrenheit. Use the temperature calculator.

1. Use the ideal gas law to calculate the partial pressure of each gas by substituting the values of moles (ni), temperature (T), and volume (V) into the formula.

Example:

Suppose we have a mixture of three gasses with the following moles: 2 moles of gas A, 3 moles of gas B, and 1 mole of gas C. The temperature is 298 K, and the volume is 5 L.

Given data:

Moles: Gas A (2), Gas B (3), and Gas C (1)

Temperature: 298k

Volume: 5L

Calculation:

• Calculate the partial pressure of gas A:

PA = (2 mol * 0.0821 Latm/molK * 298 K) / 5 L = 9.712 atm

• Calculate the partial pressure of gas B:

PB = (3 mol * 0.0821 Latm/molK * 298 K) / 5 L = 14.568 atm

• Calculate the partial pressure of gas C:

PC = (1 mol * 0.0821 Latm/molK * 298 K) / 5 L = 4.856 atm

Real-life applications of partial pressure:

Breathing and blood gasses: The partial pressure of oxygen and carbon dioxide in the blood determines the breathing rate.

Scuba diving: The partial pressure of gasses in the breathing mixture is critical for divers to avoid decompression sickness and other diving-related complications.

Chemical reactions: In many industrial processes, the partial pressure of gasses is used to control reaction rates, as it affects the rate of reaction and product yields.

Meteorology: The partial pressure of water vapor in the atmosphere determines the relative humidity, which plays a role in weather forecasting and understanding climate patterns.