Question

A sample of ozone gas is found to be \(40 \%\) dissociated into oxygen. The average molecular mass of sample should be

Short answer

Answer: The average molecular mass of the ozone sample is 41.6 g/mol.

Step-by-step solution

Identify the mass of ozone and oxygen molecules

To find the average molecular mass of the sample, we first need to know the molecular weights of ozone and oxygen. The molecular weight of an oxygen atom is 16 g/mol. The molecular weight of ozone (O3) is 3 times the atomic weight of oxygen, and the molecular weight of oxygen (O2) is 2 times the atomic weight of oxygen. So, the molecular weight of ozone (O3) is: #\( 3 \times 16 \)= 48 g/mol#. The molecular weight of oxygen (O2) is: #\( 2 \times 16 \)= 32 g/mol#.

Calculate the proportional mass of ozone and oxygen molecules

We know that the sample of ozone is 40% dissociated into oxygen. Therefore, 60% of the sample remains ozone, and 40% of the sample is now oxygen. Proportional mass of ozone in the sample: #0.6 \times 48 g/mol = 28.8 g/mol#. Proportional mass of oxygen in the sample: #0.4 \times 32 g/mol = 12.8 g/mol#.

Calculate the average molecular mass of the sample

To find the average molecular mass of the sample, we will add the proportional mass of both ozone and oxygen molecules. Average molecular mass of the sample: #28.8 + 12.8 = 41.6 g/mol#. So, the average molecular mass of the given ozone sample, which is 40% dissociated into oxygen, is 41.6 g/mol.

Key concepts

ozone dissociation

Ozone dissociation is a chemical process where ozone molecules, which are triatomic molecules composed of three oxygen atoms (O₃), break down into diatomic oxygen molecules (O₂). This process occurs in various atmospheric and laboratory conditions and can significantly impact the properties of a gaseous sample. Imagine a scenario where a certain percentage of ozone gas in a given volume breaks apart into oxygen molecules. The degree to which this dissociation happens can affect how we calculate the average molecular mass of the sample.

• In our exercise, the ozone sample is 40% dissociated. This means that 40% of the original ozone molecules have broken down into oxygen molecules.
• Understanding this proportion helps us to calculate the new average molecular mass of the sample after dissociation.

By knowing the extent of dissociation, we can adjust our calculations to reflect the mix of molecules present in the final gas sample.

molecular weight calculation

Molecular weight calculation involves determining the weight of a molecule by adding the atomic weights of every element in it. In our example, we're dealing with gases like ozone (O₃) and oxygen (O₂). Here's how the calculation is done:

• The atomic weight of a single oxygen atom is 16 g/mol.
• For ozone (O₃), which consists of three oxygen atoms: \[ \text{Molecular weight of O₃} = 3 \times 16 = 48\, \text{g/mol} \]
• For diatomic oxygen (O₂), which has two oxygen atoms: \[ \text{Molecular weight of O₂} = 2 \times 16 = 32\, \text{g/mol} \]

Once you determine these individual molecular weights, you can then calculate the average molecular mass of any sample, considering the proportions of different molecules present due to dissociation. This requires multiplying each molecule's weight by its percentage in the mixture and summing these products to get a weighted average.

oxygen molecule

The oxygen molecule, often referred to chemically as O₂, plays a critical role in both the natural environment and various chemical calculations. It is the simplest form of molecular oxygen and is made up of two oxygen atoms bonded together. This makes it a diatomic molecule.

• Its molecular weight is derived from the weight of two oxygen atoms: \(2 \times 16\, \text{g/mol} = 32\, \text{g/mol}\) . This is essential information for tasks like calculating the change in molecular mass due to ozone dissociation.
• In our scenario where ozone dissociates, the production of O₂ must be accounted for to understand the changes in the average molecular mass of the gas mixture.

This understanding of oxygen molecules assists in predicting the behavior and properties of gases in both scientific and real-world contexts.