Answer : The final temperature of the solution is, [tex]41.4^oC[/tex]
Explanation :
First we have to calculate the heat produced.
[tex]\Delta H=\frac{q}{n}[/tex]
where,
[tex]\Delta H[/tex] = enthalpy change = 81.5 kJ/mol
q = heat released = ?
m = mass of [tex]CaCl_2[/tex] = 15.0 g
Molar mass of [tex]CaCl_2[/tex] = 110.98 g/mol
[tex]\text{Moles of }CaCl_2=\frac{\text{Mass of }CaCl_2}{\text{Molar mass of }CaCl_2}=\frac{15.0g}{110.98g/mole}=0.135mole[/tex]
Now put all the given values in the above formula, we get:
[tex]81.5kJ/mol=\frac{q}{0.135mole}[/tex]
[tex]q=11.0kJ[/tex]
Now we have to calculate the final temperature of solution in the calorimeter.
[tex]q=m\times c\times (T_2-T_1)[/tex]
where,
q = heat produced = 11.0 kJ = 11000 J
m = mass of solution = 15.0 + 145 = 160.0 g
c = specific heat capacity of water = [tex]4.18J/g^oC[/tex]
[tex]T_1[/tex] = initial temperature = [tex]25.0^oC[/tex]
[tex]T_2[/tex] = final temperature = ?
Now put all the given values in the above formula, we get:
[tex]11000J=160.0g\times 4.18J/g^oC\times (T_2-25.0)[/tex]
[tex]T_2=41.4^oC[/tex]
Thus, the final temperature of the solution is, [tex]41.4^oC[/tex]
When a 15.0-g sample of CaCl₂ is dissolved in 145 g water, both substances at 25.0°C, the final temperature of the solution is 41.4 °C.
Let's consider the thermochemical equation for the dissolution of CaCl₂:
CaCl₂(s) → Ca²⁺(aq) + 2 Cl⁻(aq) ∆H = -81.5 kJ/mol
We can calculate the heat released by the dissolution (Qd) of 15.0 g of CaCl₂ considering that:
[tex]Qd = 15.0 g \times \frac{1mol}{110.98g} \times \frac{(-81.5kJ)}{mol} = -11.0 kJ[/tex]
According to the law of conservation of energy, the sum of the heat released by the dissolution (Qd) and the heat absorbed by the solution (Qs) is zero.
[tex]Qd + Qs = 0\\\\Qs = -Qd = 11.0 kJ[/tex]
We can calculate the final temperature of the solution using the following expression.
[tex]Qs = c \times m \times (T2-T1)\\\\T2 = \frac{Qs}{c \times m} + T1 = \frac{11.0 \times 10^{3}J }{\frac{4.18J}{\° C.g } \times (15.0g+145g)} + 25.0\° C = 41.4 \° C[/tex]
where,
When a 15.0-g sample of CaCl₂ is dissolved in 145 g water, both substances at 25.0°C, the final temperature of the solution is 41.4 °C.
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