There are five parameters in ideal gas law equation (PV = nRT). When you know four parameters, you can find the unknown parameter in the equation. Ideal gas law questions are asked frequently in physical chemistry papers and air problems.

You can use following calculator to calculate unknown parameter in PV = nRT equation. Keep empty unknown parameter field.

Answer

Parameters of equation are given below with their units.

- P = Pressure (Pa)
- V = Volume (m
^{3}) - n = Amount (mol)
- R = Universal gas constant (J mol
^{-1}K^{-1}) = 8.314 J mol^{-1}K^{-1} - T = Temperature (K)

**Question**

- Calculate the amount of gas containing inside the tank.
- Calculate the mass of gas containing inside the tank.

*additional data: R = 8.314 J mol ^{-1} K^{-1}, Molar mass of gas = 28 g mol^{-1}*

**Answer**

Temperature was given in celsius. **Convert it to Kelvin as below.**.

Temperature = 27 + 273 = 300 K

Drawing a figure is a good way to illustrate the question. Write down all the data provided with units.

We know the date of pressure, volume and temperature. Then, we can substitute those values in PV = nRT equation to find the amount.

- PV = nRT
- 300 * 10
^{3}* 8.314 * 10^{-3}= n * 8.314 * 300 - n = 1 mol

Above question was a straightforward one. now we are going to discuss little bit difficult question.

**If above tank is connected with another empty tank (B) with same volume through a short pipeline, what is the pressure of
the overall system when system is still at 300K?**

The gas amount is now distributed in two tanks.

- New volume of system (V')= volume of tank A + volume of tank B

V' = 8.314 + 8.314

V' = 16.628 dm^{3} - Temperature = 300K
- Amount of gas = 1 mol

**Now, we can apply ideal gas law equation to find the pressure (P') of the system.**

- P'V' = nRT
- P' * 16.628 * 10
^{-3}= 1 * 8.314 * 300 - P' = 150 000 Pa
- P' = 150 kPa

10g of calcium carbonate crystals are heated to a high temperature in a closed container until all calcium carbonate
decomposes to calcium oxide and carbon dioxide gas. After decomposition was completed, heating was stopped and container
was put to reach to the room temperature. Initially, there were not gases inside the container. After heating the
calcium carbonate crystals, remaining solid was weighed and it was 4g. If volume of container is 8314 cm^{3}, calculate
the pressure inside the container at room temperature (25^{0}C).

From given date, we know the volume and temperature of PV = nRT. Therefore, we need to find out amount (n) before finding the pressure of the container.

For that, we can use chemical equation and weight of calcium carbonate.

**Decomposed CaCO _{3} amount = produced CO_{2} amount**

- Decomposed CaCO
_{3}amount = Decomposed CaCO_{3}mass / molar mass of CaCO_{3} - Decomposed CaCO
_{3}amount = 10 / 100 - Decomposed CaCO
_{3}amount = 0.1 mol - Therefore, produced CO
_{2}amount = 0.1 mol

Now, we know the gas amount (n) and can apply the values in PV = nRT equation.

- PV = nRT
- P * 8314 * 10
^{-6}= 0.1 * 8.314 * 298 - P = 29.8 * 10
^{3}Pa - P = 29.8 kPa

- CO
_{2}behaves as a ideal gas. - Volume of solid compound is negligible. Therefore, it is considered as total volume of container is taken by the
CO
_{2}gas.

**Question:**There are two gases (A and B) in a closed container (1 m^{3}) at
127^{0}C. Amount of gases of A and B are 10 mol and 20 mol respectively. Calculate followings.

- Total pressure in the system
- Partial pressure of A
- Partial pressure of B

**Answer**

We can solve this question in two ways.

- Method 1: Finding total pressure by assuming there is only one gas in the container
- Method 2: Finding total pressure by adding partial pressure of A and B gases

Total pressure in the system is given by the summation of partial pressures of both gases.

- P
_{T}= total pressure in the system - P
_{T}= P_{A}+ P_{B}

Because, we assume that A and B gases behave as ideal gases. Therefore, we can apply ideal gas law for the overall system considering there are total of 30 mol in the system.

- P
_{T}V = nRT - P
_{T}* 1 = 30 * 8.314 * 400 - P
_{T}= 99768 Pa - P
_{T}= 99.768 kPa

In this method, we apply ideal gas law in two occasions for A and B gases to find partial pressures of A and B gases.

- P
_{A}V = nRT - P
_{A}* 1 = 10 * 8.314 * 400 - P
_{A}= 33256 Pa - P
_{A}= 33.256 kPa

- P
_{B}V = nRT - P
_{B}* 1 = 20 * 8.314 * 400 - P
_{B}= 66512 Pa - P
_{B}= 66.512 kPa

Now, we can add partial pressures of A and B gases to find total pressure.

- P
_{T}= total pressure in the system - P
_{T}= P_{A}+ P_{B} - P
_{T}= 33.256 kPa + 66.512 kPa - P
_{T}= 99.768 kPa

**There are two gases (A and B) which react with each other as below.**

A + B → C

In a specified industry, a mixture of C and B gases is required and above reaction is proposed to use to get that mixture.

Both gases are stored in two separate containers which have same volume. A gas is at 100 kPa and B gas is at 200kPa.
Both containers were heated separately to 227^{0}C and then mixed with each other to react. Containers were
kept at 227^{0}C continuously until reaction is completed.
Volume of one container is 8.314 m^{3}.

- Calculate amount of A gas.
- Calculate amount of B gas.
- After the completion of the reaction, calculate how much (in mol) B gas is remaining and C gas was produced.
- What is the final pressure after the completion of reaction?

**Answer:**

First two parts of this question is very easy and we have already did those kind of questions earlier in this tutorial. For first two sections, pressure, volume and temperature values are given for each gas and we just need to find the amount of each gas by applying PV = nRT.

- P
_{A}V = nRT - 100 * 10
^{3}* 8.314 = n_{A}* 8.314 * 500 - n
_{A}= 200 mol

- P
_{B}V = nRT - 200 * 10
^{3}* 8.314 = n_{B}* 8.314 * 500 - n
_{B}= 400 mol

Now, we know the initial amount of A and B gases. So, we should find now the reacting amount of A and B gas as below.

Answer for part 3,

- Remaing amount of B = 200 mol
- Prodiced amount of C = 200 mol

In the end of the reaction, only B and C gases are remaining.

Because temperature is maintained at 227^{0}C (500K) and total gases amount, volume of containers are known, we can find the final pressure of the container after the reaction.

- P
_{final}V = nRT - P
_{final}* 8.314 = 400 * 8.314 * 500 - P
_{final}= 200,000 Pa - P
_{final}= 200 kPa

Here, you can try some MCQ questions relavant to PV = nRT

An ideal gas is filled to a constant volume container (1 dm^{3}) at 27^{0}C temperature. When internal pressure is reached upto 1 bar, filling is stoped and container is sealed. How much (mol) gas is fiiled to the container.

- 0.08 mol
- 0.1 mol
- 0.01 mol
- 0.04 mol
- 0.2 mol

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