### Van Dar Waals Calculator:

This online van der Waals calculator is based on the van der Waals equation of state. It is obtained by modifying the ideal gas equation of state.

The van der Waals equation is a better approximation of a real gas than the ideal gas law.

To use the van der Waals calculator, enter three known quantities and two material-specific constants to calculate the fourth quantity. To perform the calculations, the calculator uses the integrated gas law formula discussed below.

The van der Waals equation calculator supports imperial and metric units for volume and pressure and 5 temperature scales:

Kelvin, Celsius, Fahrenheit, Rankin and Reamer, as input and output.

This theory assumes that a gas consists of spherical particles of considerable size and takes into account intermolecular forces.

Note that for a given value of P, a, b, n, T there are 3 distinct solutions of V. Vol.), but only one is represented here.

### Van Dar Waals Formula:

Van dar waals equation pressure p_{(pa)} in pascal and addition the number of moles n^{2}_{(m)} in meter and multiply the Vander waal’s constant a _{(atm L2/mol )} in atm length per mole and divided by the volume v^{2}_{(m3)} in meter^{3} and multiply the volume v_{(m3)} in meter^{3} and minus the number n_{(m)} in mole and multiply the b_{(l/mol)} in length per mole is equal to the number n_{(m)} in meter and multiply the universal gas constant R and multiply the temperature T_{(k)} in Kelvin.Hence the van dar waals equation can be written as

(p_{(pa)}+n^{2}_{(m)}*a _{(atm L2/mol )} /v^{2}_{(m3)})(v_{(m3)}-n_{(m)}*b_{(l/mol)})=n_{(m)}*R*T_{(k)}

P=pressure in pascal

V=volume in meter3

A,b=Vander waal’s constant(a=4.17 atm L^{2}/mol and b=0.0371 L/mol

N=number of moles

R=universal gas constant

T=temperature in Kelvin

### Example:1

Determine the pressure of the gas using the van der waals equation where 2mole of ammonia fills 8 litre bottle at a temperature of 450k(a=4.17 atm L^{2}/mol^{2} and b=0.0371 L/mol

### Answer:

Given that a=4.17 atm L^{2}/mol^{2}

B=0.0371 L/mol

N=2

V= 8 litre

T=450k

We know that van der waals equation is

(p+a*n^{2}/v^{2})(V-nb)=nRT

By rearranging the above formula to find the pressure, the formula becomes

P=n*R*T /V-nb –n^{2}*a/v^{2}

Now substitute the values in the formula we get

P=(2)(0.0821)(450)/8-(2)(0.0371)-2^{2}(4.17)/8^{2}

P=8.901425 atm

Thus,the pressure of the real gas using van der waals=8.901425 atm

### Example:2

Determine the pressure of the gas using the van der waals equation where 3mole of ammonia fills 7 litre bottle at a temperature of 250k(a=4.17 atm L^{2}/mol^{2} and b=0.0371 L/mol

### Answer:

Given that a=4.17 atm L^{2}/mol^{2}

B=0.0371 L/mol

N=3

V=7litre

T=250k

We know that van der waals equation is

(p+a*n^{2}/v^{2})(V-nb)=nRT

By rearranging the above formula to find the pressure, the formula becomes

P=n*R*T /V-nb –n^{2}*a/v^{2}

Now substitute the values in the formula we get

P=(3)(0.0821)(250)/7-(3)(0.0371)-3^{2}(4.17)/7^{2}

P=7.919210 atm

Thus,the pressure of the real gas using van der waals=7.919210atm