Respuesta :
Answer : The enthalpy change for the solution is 166.34 kJ/mol
Explanation :
First we have to calculate the enthalpy change of the reaction.
Formula used :
[tex]\Delta H=mC\Delta T\\\\\Delta H=mC(T_2-T_1)[/tex]
where,
[tex]\Delta H[/tex] = change in enthalpy = ?
C = heat capacity of water = [tex]4.18J/g.K[/tex]
m = total mass of sample = 2.174 + 127.4 = 129.6 g
[tex]T_1[/tex] = initial temperature = [tex]23^oC=273+23=296K[/tex]
[tex]T_2[/tex] = final temperature = [tex]37.1^oC=273+37.1=310.1K[/tex]
Now put all the given values in the above expression, we get:
[tex]\Delta H=mC(T_2-T_1)[/tex]
[tex]\Delta H=129.6g\times 4.18J/g.K\times (310.1-296)K=7638.36J[/tex]
Now we have to calculate the moles of AX added to water.
[tex]\text{ Moles of }AX=\frac{\text{ Mass of }AX}{\text{ Molar mass of }AX}=\frac{2.714g}{59.1097g/mole}=0.04592moles[/tex]
Now we have to calculate the enthalpy change for the solution.
As, 0.04592 moles releases heat = 7638.36 J
So, 1 moles releases heat = [tex]\frac{7638.36}{0.04592}=166340.59J=166.34kJ[/tex]
Therefore, the enthalpy change for the solution is 166.34 kJ/mol
When 2.714 g of AX(s) dissolves in 127.4 g of water in a coffee-cup calorimeter and the temperature rises from 23.3 °C to 37.1 °C, the enthalpy change for the solution process is -163 kJ/mol.
A coffee cup calorimeter is a constant-pressure calorimeter. As such, the heat that is measured in such a device is equivalent to the change in enthalpy.
A solution is prepared by dissolving 2.714 g of AX (solute) in 127.4 g of water (solvent). The mass of the solution (m) is:
[tex]m = 2.714g + 127.4 g = 130.1 g[/tex]
When AX is dissolved, the temperature of the system rises from 23.3 °C to 37.1 °C. Assuming the solution has the same specific heat as water (c = 4.18 J/g.K = 4.18 J/g.°C), we can calculate the heat absorbed by the calorimeter using the following expression.
[tex]Q = c \times m \times \Delta T = \frac{4.18J}{g. \° C } \times 130.1 g \times (37.1 \° C - 23.3 \° C) = 7.50 \times 10^{3} J = 7.50 kJ[/tex]
According to the law of conservation of energy, the sum of the heat absorbed by the calorimeter (Qcal) and the heat released by the solution (Qsol) is zero.
[tex]Qcal + Qsol = 0\\Qsol = -Qcal = -7.50 kJ[/tex]
2.714 g of AX(s) with a molar mass of 59.1097 g/mol are dissolved. The corresponding moles are:
[tex]2.714 g \times \frac{1mol}{59.1097g} = 0.04591 mol[/tex]
Finally, we can calculate the enthalpy change (in kJ/mol) for the solution process using the following expression.
[tex]\Delta Hsol = \frac{Qsol}{n} = \frac{-7.50 kJ}{0.04591mol} = -163 kJ/mol[/tex]
When 2.714 g of AX(s) dissolves in 127.4 g of water in a coffee-cup calorimeter and the temperature rises from 23.3 °C to 37.1 °C, the enthalpy change for the solution process is -163 kJ/mol.
You can learn more about calorimetry here: https://brainly.com/question/1407669
