# How to Calculate and Solve for Temperature, Number of Moles, Volume, Van’t Hoff Factor and Osmotic Pressure | The Calculator Encyclopedia

**Last Updated on February 18, 2024**

The image above represents the osmotic pressure. To calculate the osmotic pressure, five parameters are needed and these parameters are I**deal Gas Constant (R)**, **Temperature in Kelvin (T)**, **Number of Moles (n), Volume (V), **and **Van’t Hoff’s Factor ****(i).**

The formula for calculating osmotic pressure:

π = i ^{nRT} ⁄ _{V}

Where;

π = osmotic pressure

n = number of moles

R = ideal gas constant

T = temperature in Kelvin

i = Van’t Hoff’s Factor

V = Volume

Let’s solve an example;

Find the osmotic pressure when the ideal gas constant is 0.08206 with a temperature in kelvin of 120, the number of moles is 32, a volume of 48, and a van’t hoff’s factor of 24.

This implies that;

n = number of moles = 32

R = ideal gas constant = 0.08206

T = temperature in Kelvin = 120

i = Van’t Hoff’s Factor = 24

V = Volume = 48

π = i ^{nRT} ⁄ _{V}

π = 24 ^{32 x 0.08206 x 120} ⁄ _{48}

That is, π = (24) ^{(315.110)} ⁄ _{(48)}

π = (24)(6.5647)

π = 157.5

Therefore, the **osmotic pressure **is **157.5 atm.**

**Calculating the Van’t Hoff’s Factor using the Osmotic Pressure, Number of Moles, Temperature in Kelvin, Ideal Gas Constant and Volume**

i = ^{Vπ} / _{nRT}

Where;

i = Van’t Hoff’s Factor

π = osmotic pressure

V = Volume

n = number of moles

R = ideal gas constant

T = temperature in Kelvin

Let’s solve an example;

Find the Van’t Hoff’s Factor when the osmotic pressure is 220, volume of 50, temperature in kelvin of 180, and the number of moles of 60. (R = 0.08206)

This implies that;

π = osmotic pressure = 220

V = Volume = 50

n = number of moles = 60

R = ideal gas constant = 0.08206

T = temperature in Kelvin = 180

i = ^{Vπ} / _{nRT}

i = ^{50 x 220} / _{60 x 0.08206 x 180}

That is, i = ^{11000} / _{866.808}

i = 12.69

Therefore, the **Van’t Hoff’s Factor **is **12.69.**

**Calculating the Volume using the Osmotic Pressure, Number of Moles, Temperature in Kelvin, Ideal Gas Constant, and Van’t Hoff’s Factor**

V = ^{i (nRT)} / _{π}

Where;

V = Volume

i = Van’t Hoff’s Factor

π = osmotic pressure

n = number of moles

R = ideal gas constant

T = temperature in Kelvin

Let’s solve an example;

Find the volume when the osmotic pressure is 280, Van’t Hoff’s Factor of 40, the temperature in kelvin of 90, and the number of moles of 70. (R = 0.08206)

This implies that;

i = Van’t Hoff’s Factor = 40

π = osmotic pressure = 280

n = number of moles = 70

R = ideal gas constant = 0.08206

T = temperature in Kelvin = 90

V = ^{i (nRT)} / _{π}

V = ^{40 (70 x 0.08206 x 90)} / _{280}

This means, V = ^{40 (516.978)} / _{280}

V = ^{20679.12} / _{280}

V = 73.854

Therefore, the **volume **is **73.854.**

**Calculating the Number of Moles using the Osmotic Pressure, Volume, Temperature in Kelvin, Ideal Gas Constant, and Van’t Hoff’s Factor**

n = ^{Vπ} / _{i (RT)}

Where;

n = number of moles

V = Volume

π = osmotic pressure

i = Van’t Hoff’s Factor

R = ideal gas constant

T = temperature in Kelvin

Let’s solve an example;

Find the number of moles when the osmotic pressure is 140, Van’t Hoff’s Factor of 32, the temperature in kelvin of 88, and the volume of 65. (R = 0.08206)

This implies that;

V = Volume = 65

π = osmotic pressure = 140

i = Van’t Hoff’s Factor = 32

R = ideal gas constant = 0.08206

T = temperature in Kelvin = 88

n = ^{Vπ} / _{i (RT)}

n = ^{65 x 140} / _{32 (0.08206 x 88)}

So, n = ^{9100} / _{32 (7.22128)}

n = ^{9100} / _{231.08096}

n = 39.38

Therefore, the **number of moles **is **39.38.**

**Calculating the Temperature in Kelvin using the Osmotic Pressure, Volume, Ideal Gas Constant, Number of Moles, and Van’t Hoff’s Factor**

T = ^{Vπ} / _{i (nR)}

Where;

T = temperature in Kelvin

V = Volume

π = osmotic pressure

i = Van’t Hoff’s Factor

n = number of moles

R = ideal gas constant

Let’s solve an example;

Given that osmotic pressure is 90, Van’t Hoff’s Factor of 22, the number of moles of 12, and the volume of 60. (R = 0.08206). Find the temperature in kelvin.

This implies that;

V = Volume = 60

π = osmotic pressure = 90

i = Van’t Hoff’s Factor = 22

n = number of moles = 12

R = ideal gas constant = 0.08206

T = ^{Vπ} / _{i (nR)}

T = ^{60 x 90} / _{22 (12 x 0.08206)}

Then, T = ^{5400} / _{22 (0.98472)}

T = ^{5400} / _{21.66384}

T = 249.26

Therefore, the **temperature in kelvin** is **249.26.**

**How to Calculate the Osmotic Pressure Using The Calculator Encyclopedia**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the osmotic pressure.

To get the answer and workings of the osmotic pressure using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Basic Chemistry **under **Chemistry**

Now, Click on **Osmotic Pressure** under **Basic Chemistry**

The screenshot below displays the page or activity to enter your values, to get the answer for the osmotic pressure according to the respective parameters which are the **Van’t Hoff’s Factor (i), Ideal Gas Constant (R), Temperature in Kelvin (T), Number of Moles (n)** and **Volume (V).**

Now, enter the values appropriately and accordingly for the parameters as required by the **example** above where the **Van’t Hoff’s Factor (i)** is **24**,** Ideal Gas Constant (R)** is **0.08206**,** Temperature in Kelvin (T)** is **120**,** Number of Moles (n) **is **32** and **Volume (V)** is **48.**

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator** – The Calculator Encyclopedia solves for the osmotic pressure and presents the formula, workings, and steps too.