Respuesta :
Answer : The enthalpy of reaction [tex](\Delta H_{rxn})[/tex] is, 67.716 KJ/mole
Explanation :
First we have to calculate the moles of [tex]AgNO_3[/tex] and [tex]HCl[/tex].
[tex]\text{Moles of }AgNO_3=\text{Molarity of }AgNO_3\times \text{Volume}=(0.100mole/L)\times (0.05L)=0.005mole[/tex]
[tex]\text{Moles of }HCl=\text{Molarity of }HCl\times \text{Volume}=(0.100mole/L)\times (0.05L)=0.005mole[/tex]
Now we have to calculate the moles of AgCl formed.
The balanced chemical reaction will be,
[tex]AgNO_3(aq)+HCl(aq)\rightarrow AgCl(s)+HNO_3(aq)[/tex]
As, 1 mole of [tex]AgNO_3[/tex] react with 1 mole of [tex]HCl[/tex] to give 1 mole of [tex]AgCl[/tex]
So, 0.005 mole of [tex]AgNO_3[/tex] react with 0.005 mole of [tex]HCl[/tex] to give 1 mole of [tex]AgCl[/tex]
The moles of AgCl formed = 0.005 mole
Total volume of the solution = 50.0 ml + 50.0 ml = 100.0 ml
Now we have to calculate the mass of solution.
Mass of the solution = Density of the solution × Volume of the solution
Mass of the solution = 1.00 g/ml × 100.0 ml = 100 g
Now we have to calculate the heat.
[tex]q=m\times C\Delta T=m\times C \times (T_2-T_1)[/tex]
where,
q = heat
C = specific heat capacity = [tex]4.18J/g^oC[/tex]
m = mass = 100 g
[tex]T_2[/tex] = final temperature = [tex]24.21^oC[/tex]
[tex]T_1[/tex] = initial temperature = [tex]23.40^oC[/tex]
Now put all the given values in the above expression, we get:
[tex]q=100g\times (4.18J/g^oC)\times (24.21-23.40)^oC[/tex]
[tex]q=338.58J[/tex]
Now we have to calculate the enthalpy of the reaction.
[tex]\Delta H_{rxn}=\frac{q}{n}[/tex]
where,
[tex]\Delta H_{rxn}[/tex] = enthalpy of reaction = ?
q = heat of reaction = 338.58 J
n = moles of reaction = 0.005 mole
Now put all the given values in above expression, we get:
[tex]\Delta H_{rxn}=\frac{338.58J}{0.005mole}=6771.6J/mole=67.716KJ/mole[/tex]
Conversion used : (1 KJ = 1000 J)
Therefore, the enthalpy of reaction [tex](\Delta H_{rxn})[/tex] is, 67.716 KJ/mole
For this reaction, the heat of reaction is -67.8 KJ/mol.
The equation of the reaction is;
AgNO3(aq) + HCl(aq) -----> AgCl(s) + HNO3(aq)
Number of moles of AgNO3 = 50/1000 L × 0.100 M = 0.005 M
Number of moles of HCl = 50/1000 L × 0.100 M = 0.005 M
Temperature change = 24.21 °C - 23.40 °C = 0.81°C
Total volume of solution = 50.0 mL + 50.0 mL = 100 mL
Since the density of solution= 1.00 g/mL
Total mass of solution = 100g
Heat absorbed by solution = mcθ
m = mass of solution
c = specific heat capacity of solution
θ = temperature change
Heat absorbed by solution = 100g × 4.18 J/g ∙ °C × 0.81°C = 0.339 KJ
ΔHrxn = -( 0.339 KJ)/ 0.005 M
ΔHrxn = -67.8 KJ/mol
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