Respuesta :
Answer : The final temperature of the mixed solutions will be, [tex]24.76^oC[/tex]
Explanation :
First we have to calculate the moles of [tex]HCl[/tex] and [tex]Ba(OH)_2[/tex].
[tex]\text{Moles of }HCl=\text{Molarity of }HCl\times \text{Volume of solution}=0.461mole/L\times 0.2L=0.0922mole[/tex]
[tex]\text{Moles of }Ba(OH)_2=\text{Molarity of }Ba(OH)_2\times \text{Volume of solution}=0.231mole/L\times 0.2L=0.0462mole[/tex]
Now we have to calculate the limiting reactant.
The balanced chemical reaction will be,
[tex]2HCl+Ba(OH)_2\rightarrow BaCl_2+2H_2O[/tex]
As, 1 mole of [tex]Ba(OH)_2[/tex] react with 2 mole of HCl
So, 0.0462 mole of [tex]Ba(OH)_2[/tex] react with [tex]2\times 0.0462=0.0924[/tex] mole of HCl
From this we conclude that, [tex]HCl[/tex] is an excess reagent because the given moles are greater than the required moles and [tex]Ba(OH)_2[/tex] is a limiting reagent and it limits the formation of product.
Now we have to calculate the moles of water.
From the balanced chemical reaction, we conclude that
As, 1 mole of [tex]Ba(OH)_2[/tex] react to give 2 moles of [tex]H_2O[/tex]
So, 0.0462 mole of [tex]Ba(OH)_2[/tex] react to give [tex]2\times 0.0462=0.0924[/tex] moles of [tex]H_2O[/tex]
The moles of water = 0.0924 mole
Now we have to calculate the heat released.
As, 1 mole of water releases heat = 56.2 KJ/mole
So, 0.0924 mole of water releases heat = [tex]0.0924\times 56.2KJ/mole=5.19288KJ=5192.88J[/tex]
Now we have to calculate the final temperature of solution.
[tex]q=m\times c\times (T_{final}-T_{initial})[/tex]
where,
q = amount of heat = 5192.88 J
[tex]c[/tex] = specific heat capacity = [tex]4.18J/g^oC[/tex]
The volume of water = 200 ml + 200 ml = 400 ml
As the density of water is, 1 g/ml.
So, the mass of water = [tex]1g/ml\times 400ml=400g[/tex]
[tex]T_{final}[/tex] = final temperature = ?
[tex]T_{initial}[/tex] = initial temperature = [tex]21.66^oC[/tex]
Now put all the given values in the above formula, we get:
[tex]5192.88J=400g\times 4.18J/g^oC\times (T_{final}-21.66)^oC[/tex]
[tex]T_{final}=24.76^oC[/tex]
Therefore, the final temperature of the mixed solutions will be, [tex]24.76^oC[/tex]
