## What is the Molar Volume of a Gas at STP?

## The Mole and the Volume of Gas

- It is rather tricky to find the number of moles of a gas by weighing its mass. Chemists determine the number of moles of any
**gas**by measuring its volume. However, this cannot be done for solids and liquids. - It is found that under the same temperature and pressure, equal volumes of all gases contain the same number of particles. Therefore, chemists introduced the concept of molar volume.
**Molar volume**of a gas is defined as the volume of one mole of the gas.- Thus, the molar volume is also the volume occupied by 6.02 x 10
^{23}particles of gas. - The molar volume of any gas is 22.4 dm
^{3}mol^{-1}at STP or 24 dm^{3}mol^{-1}at room conditions.

**Note:**STP refers to**standard temperature**of 0°C and pressure of 1 atmosphere. Room conditions refer to the temperature of 25°C and the pressure of 1 atmosphere. - This means that one mole of any gas occupies the same volume at STP, which is 22.4 dm
^{3}. Under room conditions, one mole of any gas occupies 24 dm^{3}.

Figure above Each of these balloons contains 6.02 x 10^{23}gas molecules. - The following relationship shows how the volume of a gas can be converted to the number of moles and vice versa.

- In calculations, make sure that the volume of gas and the molar volume are of the same unit, that is, both are in cm
^{3}or both are in dm^{3}. Remember,**1 dm**^{3}= 1000 cm^{3}

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## The Mole and the Volume of Gas Problems with Solutions

**1. What is the volume of 0.4 mole of carbon dioxide gas at STP?**

**[Molar volume: 22.4 dm ^{3} mol^{-1} at STP]**

**Solution:**

Given the number of moles of carbon dioxide, CO

_{2}= 0.4 mol

Therefore, the volume of CO

_{2}= number of moles of CO

_{2}x molar volume at STP

= 0.4 x 22.4 dm

^{3}= 8.96 dm

^{3}

**2. Find the number of moles of ammonia gas contained in a sample of 60 cm ^{3} of the gas at room conditions. [Molar volume: 24 dm^{3} mol^{-1} at room conditions]**

**Solution:**

## The Relationship Between Mole, Number of particles, Mass and Volume

The following shows the relationships between the number of moles, number of particles, mass and volume of gases.

In most calculations, we first convert other quantities such as the number of particles, mass or volume to the number of moles (refer to Table).

**Table: Summary of steps in calculations involving the number of moles**

Conversion | Steps |

From mass to volume | Mass → number of moles → volume |

From volume to mass | Volume → number of moles → mass |

From volume to number of particles | Volume → number of moles → number of particles |

From number of particles to volume | Number of particles → number of moles → volume |

## The Relationship Between Mole, Number of particles, Mass and Volume Problems with Solutions

**1. What is the volume of 12 g of methane at STP? **

**[Relative atomic mass: H, 1; C, 12. Molar volume: 22.4 dm ^{3} mol^{-1} at STP]**

**Solution:**

**2. A sample of 120 cm ^{3} of carbon dioxide is collected at room conditions in an experiment. Calculate the mass of the sample of carbon dioxide.**

**[Relative atomic mass: C, 12; O, 16. Molar volume: 24 dm**

^{3}mol^{-1}at room conditions]**Solution:**

Given the volume of carbon dioxide, CO

_{2}= 120 cm

^{3}= 120/1000 dm

^{3}= 0.12 dm

^{3}

Therefore, the mass of CO

_{2}= number of moles of CO

_{2}× molar mass of CO

_{2}= 0.005 × [12 + 2(16)]

= 0.005 × 44

= 0.22 g

**3. How many hydrogen molecules are there in 6 dm ^{3} of hydrogen gas at room conditions? [Molar volume: 24 dm^{3} mol^{-1} at room conditions. Avogadro constant, NA: 6.02 × 10^{23} mol^{-1}]**

**Solution:**

**4. Find the volume of nitrogen gas in cm ^{3} at STP that consists of 2.408 × 10^{23} nitrogen molecules. [Molar volume: 22.4 dm^{3} mol^{-1} at STP. Avogadro constant, Na: 6.02 × 10^{23} mol^{-1}]**

**Solution:**