the vapour density of a mixture containing no2 and n2o4 is 38.3 at 27°C. The moles of NO2 in 100 moles of mixture are

To find the moles of NO2 in the mixture containing NO2 and N2O4, we can use the concept of vapor density and the ideal gas law. The vapor density gives us a way to relate the mass of the gas mixture to the number of moles and the molecular weights of the components involved.

Understanding Vapor Density

The vapor density (VD) of a gas mixture is defined as the mass of the gas per unit volume compared to the mass of an equal volume of hydrogen at the same temperature and pressure. The formula for vapor density can also be expressed in terms of molar mass:

VD = (M_mixture) / (M_H2)

Here, M_H2 (the molar mass of hydrogen) is approximately 2 g/mol. Therefore:

M_mixture = VD × 2

Calculating the Molar Mass of the Mixture

Given that the vapor density of the mixture is 38.3, we can calculate the molar mass of the mixture:

M_mixture = 38.3 × 2 = 76.6 g/mol

Determining Molar Masses of Components

Next, we need to know the molar masses of NO2 and N2O4:

• Molar mass of NO2 = 14 (N) + 2 × 16 (O) = 46 g/mol
• Molar mass of N2O4 = 2 × 14 (N) + 4 × 16 (O) = 92 g/mol

Setting Up the Equation

Let x be the number of moles of NO2 in the mixture, and since the total number of moles in the mixture is 100, the moles of N2O4 will be (100 - x). We can express the average molar mass of the mixture as follows:

M_mixture = (x × M_NO2 + (100 - x) × M_N2O4) / 100

76.6 = (x × 46 + (100 - x) × 92) / 100

Solving for x

Now we can multiply both sides by 100 to eliminate the fraction:

7660 = 46x + 9200 - 92x

Combining like terms gives us:

7660 = 9200 - 46x

Rearranging this equation results in:

46x = 9200 - 7660

46x = 540

Now, divide both sides by 46:

x = 540 / 46 ≈ 11.74

Conclusion on Moles of NO2

Thus, in the mixture of 100 moles, approximately 11.74 moles of NO2 are present. This calculation illustrates how we can use vapor density and molar masses to find the composition of a gas mixture. If you have any further questions on this topic or related concepts, feel free to ask!