Question

The oxidation of copper(I) oxide, Cu2O(s) , to copper(II) oxide, CuO(s) , is an exothermic process. 2Cu2O(s)+O2(g)⟶4CuO(s) The change in enthalpy upon reaction of 42.60 g Cu2O(s) is −43.47 kJ . Calculate the work, ???? , and energy change, Δ????rxn , when 42.60 g Cu2O(s) is oxidized at a constant pressure of 1.00 bar and a constant temperature of 25∘ C . Note that ΔErxn is sometimes used as the symbol for energy change instead of Δ????rxn .

Answer 1

Answer:

The work is  

      $W = -0.369kJ$

The energy  change of the reaction is  $\Delta U _{rxn} = 43.839 kJ$  

Explanation:

From the question we are told that

    The chemical equation for this reaction is

             $2 Cu_2 O + O_2_{(g)} ----> 4 CuO_{(s)}$

     The mass of  $Cu_2 O$ is  $m = 42.60g$

      The enthalpy $Cu_2 O$ is  $\Delta H_{re} = -43.47 \ kJ$ this also the change in energy in terms of heat

      The pressure at which it is oxidized is $P = 1\ bar$

The  no of moles of $Cu_2 O$used in this reaction is mathematically represented as

        $n = \frac{mass \ of \ Cu_2 O}{Molar \ mass \ of \ Cu_2 O}$

The molar mass of $Cu_2 O$ is  a constant with a value  $M = 143.1 g/mol$

   Now substituting values

             $n = \frac{ 42.60}{143.1}$

            $n = 0.29769 \ moles$

From the reaction we see that

Two mole of $Cu_2 O$  reacts with One mole of $O_2$ to give Four moles of  $CuO_{(s)}$

This means that

One mole of  $Cu_2 O$  reacts with 0.5 mole of $O_2$ to give two moles of  $CuO_{(s)}$

it also implies that

$0.29769 \ mole$ of  $Cu_2 O$  reacts with $0.5 * 0.29769$ moles of $O_2$ to give $2* 0.29769$ moles of  $CuO_{(s)}$

so

$0.29769 \ mole$ of  $Cu_2 O$  reacts with $0.149$ moles of $O_2$ to give $0.595$ moles of  $CuO_{(s)}$

Now the number of moles of gaseous reactant is

      $N_{O_2} = 0.149 \ moles$

The number of moles of gaseous product  is

     $N_p = 0 \ moles$

So the change in number of moles for gaseous  compounds is mathematically evaluated as

         $\Delta N = 0- 0.149 \ moles$

        $\Delta N = - 0.149 \ moles$

Now the workdone for  the compound $Cu_2 O$ is mathematically represented as

        $W = \Delta N RT$

Where R is the gas constant with a value of $R = 8.314 J/mol \cdot K$

            T is the temperature with a value  $T = 25 + 273 = 298 K$

     Substituting values

     $W = -0.149 * 8.314 * (298)$

     $W = -0.369kJ$

Generally the internal energy change of the reaction can be represented as

           $\Delta U _{rxn} = \Delta H_{re} - W$

Substituting value

        $\Delta U _{rxn} = -43.47 - (-0.369)$

        $\Delta U _{rxn} = 43.839 kJ$  

This is the internal energy change on the reaction for 42.60 g of $Cu_2 O$