Solve this:

4. If 100 moles of H₂O₂ decompose at 1 bar and 300 K, the work done (kJ) by one mole of $O_{2\left(g\right)}$ as it expends against 1 bar pressure is 

$2H_2{O}_{2\left(f\right)}\rightleftharpoons 2H_2{O}_{2\left(l\right)}+O_{2\left(g\right)}$
(R=8.3 J K^-1 mol^-1)

(a) 124.50              (b) 246.00
(c) 498.00              (d) 62.25

Dear Student,

Please find below the solution of your asked query:

According to the reaction given above, 2 moles of H₂O₂ produces 2 moles of H₂O and one mole of O₂.
So, 100 moles of H₂O₂ will produce 100 moles of H₂O and 50 moles of O₂.

Now,
         Number of moles of O₂$\left({\mathrm{n}}_{{\mathrm{O}}_2}\right)$ = 50 moles
         Gas constant (R) = 8.3 J K^-1 mol^-1
         Temperature (T) = 300 K

W = - P_ext ($∆$V)
From Ideal gas equation, PV = nRT

W = - $\left({\mathrm{n}}_{{\mathrm{O}}_2}\right)$ RT
Now, substituting the values given above;

W = - (50)(8.3)(300)
W = -124500 J
W = -124.5 kJ

Therefore, option (a) is correct.

Hope this information clears your doubts about the topic.

Keep asking!!

Regards