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**Hint:**First write the balanced reaction of iron with hydrochloric acid. For a closed vessel pressure will be constant. Then we can find the work done by following the formula. \[W = - {P_{ext}}\Delta V\]

**Complete step by step solution:**

We will calculate for the given reaction.

- The reaction between iron and hydrochloric acid gives ferrous chloride and hydrogen gas. The reaction can be given as under.

\[Fe + 2HCl \to FeC{l_2} + {H_2}\]

From the reaction, we can say that one mole of iron produces one mole of hydrogen gas.

- We know that 56 g of Fe is equivalent to 1 mole. So, 11.29 g of Fe will be equivalent to $\dfrac{{11.29}}{{56}} = 0.20$ moles.

So, 0.20 moles of hydrogen gas will be produced when 11.29 g of Fe will react with HCl.

i) If the reaction is carried out in a closed vessel, then the change in volume will be zero.

Now, we know that work can be given as

\[W = - {P_{ext}}\Delta V\]

We know that $\Delta V$ = 0.

So, W = 0.

ii) If a reaction is carried out in an open vessel, then we need to calculate the change in volume.

- The newly formed hydrogen gas would occupy some volume. The volume occupied can be given as

\[V = \dfrac{{nRT}}{P}\]

We know that number of moles n = 0.2 moles

Universal gas constant R = 0.0831 L atm/mol K

Temperature T = 298 K

and pressure P = 1 atm

So, we can write the above equation as

\[V = \dfrac{{0.2 \times 8.314 \times 298}}{1} = 4.89L\]

Thus, we can say that the change in volume $\Delta V$ = 4.89 L

So, work $W = - {P_{ext}} \times \Delta V$

So,

\[W = - 1 \times 4.89\]

So, W = -4.89 L atm

But we know that 1 L atm = 101.3 J.

So, -4.89 L atm = -4.89$ \times $ 101.3 = -495.4 J

**Thus, we obtained that the work done in a closed vessel will be zero and that in an open vessel will be equal to -495.4 J.**

**Note:**Note that iron gets oxidized to +2 oxidation state and forms $FeC{l_2}$ by the reaction with HCl. So, do not assume that iron gets oxidized to +3 oxidation state as it is also often seen in case of iron metal.

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