Consider an equimolar mixture (equal number of moles) of two diatomic gases \(\left(\mathrm{A}_{2}\right.\) and \(\mathrm{B}_{2}\) ) in a container fitted with a piston. The gases react to form one product (which is also a gas) with the formula \(\mathrm{A}_{x} \mathrm{~B}_{y}\). The density of the sample after the reaction is complete (and the temperature returns to its original state) is \(1.50\) times greater than the density of the reactant mixture. a. Specify the formula of the product, and explain if more than one answer is possible based on the given data. b. Can you determine the molecular formula of the product with the information given or only the empirical formula?

Step by step solution

01

Calculate the molar mass of the reactant mixture

Since the gases are diatomic, their molar mass would be 2A and 2B (where A and B represent the molar masses of elements A and B). The reactant mixture is equimolar, which means there are equal amounts of A₂ and B₂. Therefore, the average molar mass of the reactant mixture is: Average molar mass = \(\frac{1}{2}(2A + 2B)\)

02

Calculate the molar mass of the product

The question states that the density of the sample after the reaction is 1.50 times greater than the density of the reactant mixture. Since density is related to molar mass: Molar mass of the product = 1.50 × Average molar mass of the reactant mixture Molar mass of the product = 1.50 × \(\frac{1}{2}(2A + 2B)\) Molar mass of the product = \(1.50(A + B)\)

03

Find the empirical formula

The empirical formula of the product is AxBy. We know that the molar mass of the product is 1.50(A+B). Since the only information given is regarding the molar mass ratio of the product, we cannot determine specific values for x and y. However, we can check if more than one answer is possible based on the given data.

04

Determine if more than one answer is possible

There is more than one possibility for the formula of the product based on the given data. For example, it could be: A₁B₁ (one atom of A and one atom of B in the product) A₂B₂ (two atoms of A and two atoms of B in the product) A₃B₃ (three atoms of A and three atoms of B in the product) All these combinations could result in the molar mass of the product being 1.50 times greater than the molar mass of the reactant mixture. Result: We cannot specify the unique empirical formula of the product based on the given data as there are multiple possible combinations that fit the criteria. #b. Molecular Formula or Empirical Formula#

05

Analyze the given data

We only have information about the molar mass ratio between the product and the reactant mixture. We do not have any information about the actual elements A and B or their reaction stoichiometry.

06

Determine if the molecular formula can be deduced

Given the limited information, we cannot determine the molecular formula of the product, as we need additional data about the elements (A and B) and their stoichiometry in the reaction. Result: With the given information, we can only partially determine the empirical formula of the product, but not the molecular formula.

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