Apologies for the oversight, Mark. Let's look at the problem and address your concerns step-by-step.
The given reaction is: H2(g) + (1/2)O2(g) → H2O(g) with an enthalpy change of ΔH = -2418 kJ.
To calculate the work involved, we need to consider the change in volume associated with the reaction. Since the reaction involves gases, we can assume that the reaction will cause a change in volume inside the vessel due to the formation of water vapor.
The equation you mentioned, ΔH = ΔE + PΔV, is the correct equation to use, where ΔE represents the change in internal energy of the system, P represents the external pressure, and ΔV represents the change in volume.
You correctly observed that ΔH is approximately equal to ΔE because the reaction is carried out at constant pressure (assuming the external pressure remains constant).
However, in your calculation, you assumed that PΔV = 0. This is not accurate because work should indeed be involved. The piston would need to move to accommodate the change in volume.
To determine the work done, we can use the equation:
Work (W) = -PΔV,
where P is the pressure and ΔV is the change in volume.
To calculate the work involved, we need to determine the change in volume associated with the reaction. To do this, we can use stoichiometry and the given mass of the product.
Given: 180.16 g H2O = 10.000 mol H2O.
From the balanced equation, we can see that 1 mole of H2O(g) is formed. So, for 10.000 mol of H2O, the reaction produces a mole ratio of 10.000 mol H2O : 10.000 mol H2O.
Assuming ideal gas behavior, the change in volume (ΔV) can be calculated using the ideal gas law equation:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
In this case, we're assuming constant temperature (since it is not given), so we can rearrange the equation as:
ΔV = (n2 - n1)RT/P,
where n2 is the final number of moles (10.000 mol), n1 is the initial number of moles (0 mol, assuming no reactants are initially present), R is the ideal gas constant (0.0821 L·atm/mol·K), and P is the pressure.
Note: Make sure to use consistent units for pressure (atm) and volume (L) in the calculation.
Once you calculate the ΔV, the work (W) can be obtained by multiplying ΔV by the pressure (P). Since the problem mentions a frictionless piston and there is no external pressure mentioned, we can assume atmospheric pressure (1 atm) or state it explicitly as given in the problem.
I hope the step-by-step approach helps you with your calculation. Feel free to ask if you have any further questions or clarifications!