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.
To determine the work done by the system during the thermal decomposition of ammonium dichromate, we need to calculate the change in the number of gas moles (deltan), the gas constant (R), and the change in temperature (ΔT). The equation you mentioned, w = -deltanRT, is the correct formula to use. However, it seems that you made a calculation error.
Let's break down the steps to calculate the correct answer:
1. Calculate the value of deltan:
The balanced equation shows that 1 mole of (NH4)2Cr2O7 decomposes to produce 1 mole of N2 gas and 4 moles of H2O gas, resulting in a net change of 5 moles of gas:
deltan = 5 moles
2. Calculate the ideal gas constant (R):
The value of R depends on the units you are using. If the temperature is in Kelvin and the pressure is in atmospheres (which we assume in this case), then R = 0.0821 L·atm/(mol·K).
3. Determine the change in temperature (ΔT):
In this case, the problem specifies that the final temperature is 298 K. However, the initial temperature is not given, so we assume it is constant (meaning ΔT = 0).
4. Plug the values into the equation w = -deltanRT:
w = -(5 moles) × (0.0821 L·atm/(mol·K)) × (0 K)
= 0 J
The correct value of the work done by the system is 0 J, not 19.3 J. It is important to double-check your calculations and ensure all the given values are correctly used in the equation.