2- Gases A2 and B2 react according to the equation: A2 + B2 → AxBy . If equimolar ( not necessarily stoichiometrically equivalent) quantities are placed in a reaction vessel with a massless, frictionless piston and allowed to react to completion. The density of the gas mixture after reaction is 1.5X the original density. Find the empirical formula? Is there only one possibility? Explain.

Question

2- Gases A2 and B2 react according to the equation: A2 + B2 → AxBy . If equimolar ( not necessarily stoichiometrically equivalent) quantities are placed in a reaction vessel with a massless, frictionless piston and allowed to react to completion. The density of the gas mixture after reaction is 1.5X the original density. Find the empirical formula? Is there only one possibility? Explain.

Answer 1

I was able to find the answer - disregard this question

Answer 2

To find the empirical formula of the product formed, we need to use the given information about the density of the gas mixture after the reaction.

1. Let's assume the initial moles of A2 and B2 are both 'x' moles.
2. Since they react to completion, the product AxBy will have the same number of moles as the initial moles of A2 and B2 (x moles).
3. The density of a gas is directly proportional to its molar mass (according to the ideal gas law).
4. Since the density of the gas mixture after the reaction is 1.5 times the original density, it means the molar mass of the product is also 1.5 times the molar mass of the reactants.
5. The molar mass of A2 is 2 * Molar Mass of A (let's call it MA).
Similarly, the molar mass of B2 is 2 * Molar Mass of B (let's call it MB).
And the molar mass of AxBy is A * MA + B * MB.
6. According to the given information, (A * MA + B * MB) = 1.5 * (2 * MA + 2 * MB).

Let's solve for A and B:

A * MA + B * MB = 1.5 * (2 * MA + 2 * MB)

Now, we need to check if there is only one possibility for A and B. To check this:

1. Assume random values for A and B.
2. Calculate the left-hand side (LHS) and right-hand side (RHS) of the equation.
3. If LHS = RHS, then it is a possible solution. If not, try different values for A and B.
4. If you find any other combination of A and B that satisfies the equation, then there might be multiple possibilities. Otherwise, if you can prove that no other combination satisfies the equation, then there is only one possibility.

By following these steps, you can find the empirical formula and determine if there is only one possibility for the given equation.