# Density of gases

## Introduction

Density can be described as a substance's mass per unit volume at a particular temperature and pressure. A gas's density is also determined by its mass divided by its volume. Additionally, once you are aware of a gas's density, you may determine its molar mass. All gases density varies with temperature and pressure. In this article we will learn how to calculate gas’s density.

## What is the Density of Gas?

Gases are very responsive to changes in temperature and pressure, regardless of how slight the change may be since they are compressible, have constantly molecules are moving. Weak intermolecular interactions between the gas molecules are the main cause of how little variations in temperature and pressure affect the density of gases.

## Density Examples

Although it's common knowledge that oil and water don't mix, many individuals might not be aware that oil floats on top of the water because of its density. Oil and vinegar don't mix well in the kitchen either, and you may have seen a slimy-appearing coating on top of a salad dressing bottle. Additionally, the oil is less dense than vinegar. The practical application of oil's lesser density than water is in the event of an oil spill in the ocean.

Due to the density of helium, balloons filled with it can float above the ground, adding a festive feel to gatherings. The balloon floats because its density is lower than the surrounding air. This property is crucial for weather balloons, and it once played a crucial role in blimp and dirigible flights. Despite being the second most common element in the cosmos, helium is very uncommon on Earth due to its density.

For ocean-going ships that navigate the Arctic and Antarctic circles, icebergs provide a special challenge. Ice floats because when the temperature drops, the density of water changes. Additionally, icebergs are made of frozen freshwater, but the cold water surrounding them is salty. Because salt water is denser than freshwater and because freshwater is frozen, icebergs float when coupled with salt water. The location of the iceberg in the ocean is an issue for these ships.

## How is Density Calculated?

Although mass and density are not the same, a denser substance will usually weigh more. This is so because they are connected. The density equation is −

$$\mathrm{\rho=\frac{m}{V}}$$

ρ is the density expressed in kilograms per cubic metre, m is the mass expressed in kilograms, and V be the volume expressed in cubic metres of the object. Although grams per cubic centimetre can also be used for convenience, kilograms per cubic metre is the preferred measurement.

## Unit of Density

Density is typically a quality of a substance that can be measured, its numerical value has an impact on the calculating crucial figures. You'll notice that the definition of density uses the 2 different units of mass and volume. This implies that, such as velocity, overall density possesses derived units. Density is typically expressed in g/mL,g/cm3,g/L,and kg/L units.

## SI Unit of Density

The SI-derived unit indicates density. It is generated from the kilogram, the fundamental unit of mass in the SI, and the metre, the fundamental unit of length. The mass per unit of volume is referred to as density. Cubic metres are the SI-derived unit for volume. The resulting SI unit for density is $\mathrm{\frac{kg}{m^3}}$

## Applications of Density in Real Life

• Everyday life is full of examples of relative density, or differing densities in distinct things.

• Due to its lower density than water, wood typically floats on water. Rocks generally vanish due to being denser than water. This simple illustration demonstrates the value of science in daily life.

• A few rocks, like pumice, are light enough to float, whereas several often-utilized hardwoods, such as ebony, mahogany, and lignum vitae, are solid sufficient to sink in water. Scientifically, it doesn't matter. It is composed of wood and other stones. The relative densities of the chemicals are all matter.

• Due to vinegar's lesser density, oil floats on it.

## Ideal Gas Density Formula

A modified version of the ideal gas law is used to estimate density, replacing moles and volume with density and molar mass.

The density equivalent of the ideal gas law,

$$\mathrm{PV=dRT}$$

It employs a similar formula as the original ideal gas law,

$$\mathrm{PV=nRT}$$

Where P is the pressure in atmospheres (atm)

T is the temperature in kelvin (K)

R is the ideal gas law constant of $\mathrm{0.0821\:\frac{atm(L)}{mol(K)}}$

Precisely the same as in the previous formula, but M now refers for molar mass $\mathrm{(\frac{g}{mol})}$ and d is the density $\mathrm{(\frac{g}{L})}$

By changing the equation to $\mathrm{\frac{PM}{RT}=d}$

The units of atm, mol, and K will cancel out, remaining only the density units of $\mathrm{\frac{g}{L}}$ value.

## Solved Numerical

Q. Determine the $\mathrm{SO_2}$ gas density at 40 °C and 730 mmHg.

Ans. The molecular weight of the $\mathrm{SO_2}$ in this is 64 g/mol. We may determine the solution by putting it into the equation mentioned above.

$$\mathrm{d= \frac{P(MW)}{RT}}$$

$$\mathrm{d=\frac{730×64}{62.4×313\:K}}$$

$$\mathrm{d=2.39\:g/L}$$

So, the density of $\mathrm{SO_2}$ gas is 2.39 g/L.

## Conclusion

As you are aware, a substance's density is determined by its mass per unit volume. The density of a given gas relies on its molar mass, even though all gases occupied the same volume per mole. A gas will have a lower density if its molar mass is smaller compared to its molar mass.

## FAQs

Q1. Which gas is the least dense?

Ans. Osmium has the highest density of all the elements in the periodic table, while hydrogen has the lowest density and is a gas. Air, a combination of gases including hydrogen, carbon dioxide, and oxygen, is heavier than hydrogen.

Q2. Which gas is the heaviest?

Ans. In reality, radon is the heaviest gas, since the divalent molecule is not xenon in its natural condition in the Earth's atmosphere or crust.

Q3. What is referred to as laughing gas?

Ans. To help you unwind, nitrous oxide, a safe and efficient sedative, is combined with oxygen and inhaled through a little mask that fits over your nose. Your dentist may suggest nitrous oxide, also known as "laughing gas," to assist make you more comfortable during specific treatments.

Q4. What gas do balloons contain?

Ans. Helium or hydrogen are the lifting gases used by US pilots. Compared to air, these gases weigh less. The helium or hydrogen drawn into the envelopes of gas balloons provides them with their first lift.

Q5. Does smoke weigh more than air?

Ans. Smoke is heavier than air, but because it is hot, it usually rises to the surface. The tube allows the smoke ample time to cool before it falls to the ground like a waterfall instead of rising up.

Updated on: 26-Apr-2023

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