A popular volcano demonstration involves the thermal decomposition of ammonium dichromate: (NH4)2Cr2O7 (s) --> Cr2O3 (s) + N2 (g) + 4 H2O (g)

How much work is done by the system when 2.00 g of ammonium dichromate (M: 257.07 g/mol) completely decomposes? Assume that the final temperature is 298 K.

The answer is suppose to be +/-96.4 J.

I tried this question and got 19.3 J using w= -deltan RT.
Please tell me how to get the right answer.

mols dichromate = 2/257.07 = ?

?mols dichromate x 5 mols gas products x 22.4 L/mol x (298/273) = ? L - change in volume. Then w = -pdV = -1 atm x ?L = ? L/atm and that x 101.325 J/L-atm = -0.946

Just wondering where you got 22.4 L/mol

To calculate the work done by the system during the decomposition of ammonium dichromate, we need to consider the change in moles of gas and apply the ideal gas law. Let's break down the steps to get the correct answer:

Step 1: Calculate the moles of ammonium dichromate used.
Given that the molar mass of ammonium dichromate is 257.07 g/mol, and we have 2.00 g, we can use the formula:

moles = mass / molar mass = 2.00 g / 257.07 g/mol = 0.00777 mol

Step 2: Determine the change in moles of gas.
From the balanced equation, we can see that 1 molecule of (NH4)2Cr2O7 produces 1 molecule of N2 as a gas. Hence, the change in moles of gas during the reaction is also 0.00777 mol.

Step 3: Calculate the work done.
To calculate the work done, we can use the formula:
work = -(Δn)RT

Where:
Δn = change in moles of gas
R = ideal gas constant (8.314 J/mol·K)
T = temperature (298 K)

Substituting the values into the equation, we have:
work = -(0.00777 mol)(8.314 J/mol·K)(298 K)
work ≈ -19.33 J

It seems you reached this answer already, but the correct answer provided is +/-96.4 J. Let's evaluate if this is indeed the correct result.

Step 4: Evaluate the final solution.
Since work can be positive or negative, the answer might be correct if the system is not closed or if there is additional work involved. It's possible that the reaction occurs in an open container, allowing volume changes due to the release of gases.

However, without additional information or explanation, it's difficult to determine the precise reasoning behind the given answer. The value of +/-96.4 J should be justified within a specific context or scenario.