Question

The vapor density of N₂O₄ at a certain temperature is 30. What is the percentage dissociation of N₂O₄ at this temperature?

A. 20%
B. 30%
C. 40%
D. 50%

Answer 1

To find the percentage dissociation of N₂O₄, we can calculate the molar mass of N₂O₄ using the vapor density formula. The molar mass of N₂O₄ is equal to the vapor density multiplied by the molar mass of hydrogen gas. Once we have the molar mass of N₂O₄, we can compare the actual density of N₂O₄ with its maximum theoretical density to calculate the percentage dissociation. B. 30%

Step-by-step explanation:

The percentage dissociation of N₂O₄ can be calculated using the vapor density formula and the molar mass of N₂O₄. The formula for calculating vapor density is: vapor density = (molar mass of substance) / (molar mass of hydrogen gas). In this case, the molar mass of N₂O₄ is needed to calculate the percentage dissociation. Given that the vapor density of N₂O₄ is 30, we can find the molar mass of N₂O₄ using the formula: molar mass of N₂O₄ = vapor density * molar mass of hydrogen gas. The molar mass of hydrogen gas is 2 g/mol. Therefore, the molar mass of N₂O₄ = 30 * 2 = 60 g/mol.

Now, to find the percentage dissociation of N₂O₄, we need to compare the actual density of N₂O₄ with its maximum theoretical density. The maximum theoretical density of N₂O₄ can be calculated by assuming complete dissociation of N₂O₄ into NO₂, i.e., assuming that all of the N₂O₄ molecules dissociate into NO₂. In this case, the molar mass of N₂O₄ is multiplied by the number of moles of N₂O₄ to get the maximum theoretical density.

For example, if there are x moles of N₂O₄, the maximum theoretical density can be calculated as: maximum theoretical density = (molar mass of N₂O₄) * x. Substituting the values, we get: maximum theoretical density = 60 * x.

Answer 2

The percentage dissociation of N2O4, based on a vapor density of 30, is calculated through the stoichiometry of its dissociation reaction into NO2. Solving the corresponding equation yields a dissociation degree, which corresponds to a 40% dissociation of N2O4.

Step-by-step explanation:

The question involves the calculation of the percentage dissociation of N2O4 based on its vapor density at a certain temperature. The vapor density given is 30, which corresponds to half the molar mass if it were solely in the form of N2O4 (N2O4 has a molar mass of 92.02 g/mol, hence vapor density should be 46.01 if undissociated). Since the vapor density is lower, N2O4 must be dissociate into 2NO2 according to the following equilibrium: N2O4 → 2NO2.

To calculate the percentage dissociation, we start by assuming 1 mole of N2O4. If it partially dissociates, α moles dissociate to give α moles of N2O4 and 2α moles of NO2, where α is the degree of dissociation. The molar mass of the gas mixture is given by \((1-α)*92.02 + (2α)*46.01\). Since vapor density is half the molar mass of the mixture, 30 = \((1-α)*92.02 + (2α)*46.01)/2\), solve this equation and find α to get a percentage dissociation of 40%. Therefore, the correct option for the percentage dissociation of N2O4 is C. 40%.