<u>Answer:</u> The amount of heat absorbed by the solution is 56.98 kJ
<u>Explanation:</u>
To calculate the number of moles for given molarity, we use the equation:
.....(1)
- <u>For Barium hydroxide:</u>
Molarity of barium hydroxide solution = 0.310 M
Volume of solution = 70 mL = 0.070 L (Conversion factor: 1 L = 1000 mL)
Putting values in equation 1, we get:
![0.310M=\frac{\text{Moles of }Ba(OH)_2}{0.070L}\\\\\text{Moles of }Ba(OH)_2=(0.310mol/L\times 0.070L)=0.0217mol](https://tex.z-dn.net/?f=0.310M%3D%5Cfrac%7B%5Ctext%7BMoles%20of%20%7DBa%28OH%29_2%7D%7B0.070L%7D%5C%5C%5C%5C%5Ctext%7BMoles%20of%20%7DBa%28OH%29_2%3D%280.310mol%2FL%5Ctimes%200.070L%29%3D0.0217mol)
Molarity of HCl solution = 0.620 M
Volume of solution = 70 mL = 0.070 L
Putting values in equation 1, we get:
![0.620M=\frac{\text{Moles of HCl}}{0.070L}\\\\\text{Moles of HCl}=(0.620mol/L\times 0.070L)=0.0434mol](https://tex.z-dn.net/?f=0.620M%3D%5Cfrac%7B%5Ctext%7BMoles%20of%20HCl%7D%7D%7B0.070L%7D%5C%5C%5C%5C%5Ctext%7BMoles%20of%20HCl%7D%3D%280.620mol%2FL%5Ctimes%200.070L%29%3D0.0434mol)
The chemical equation for the reaction of NaOH and sulfuric acid follows:
![Ba(OH)_2+2HCl\rightarrow BaCl_2+2H_2O](https://tex.z-dn.net/?f=Ba%28OH%29_2%2B2HCl%5Crightarrow%20BaCl_2%2B2H_2O)
By Stoichiometry of the reaction:
2 moles of HCl produces 2 moles of water
So, 0.0434 moles of HCl will produce =
of water
- To calculate the mass of solution, we use the equation:
![\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}](https://tex.z-dn.net/?f=%5Ctext%7BDensity%20of%20substance%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20substance%7D%7D%7B%5Ctext%7BVolume%20of%20substance%7D%7D)
Density of solution = 1 g/mL
Volume of solution = [70 + 70] = 140 mL
Putting values in above equation, we get:
![1g/mL=\frac{\text{Mass of solution}}{140mL}\\\\\text{Mass of solution}=(1g/mL\times 140mL)=140g](https://tex.z-dn.net/?f=1g%2FmL%3D%5Cfrac%7B%5Ctext%7BMass%20of%20solution%7D%7D%7B140mL%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%20solution%7D%3D%281g%2FmL%5Ctimes%20140mL%29%3D140g)
- To calculate the amount of heat absorbed, we use the equation:
![q=mc\Delta T](https://tex.z-dn.net/?f=q%3Dmc%5CDelta%20T)
where,
q = heat absorbed
m = mass of solution = 140 g
c = heat capacity of solution= 4.186 J/g°C
= change in temperature = ![T_2-T_1=(25.34-21.12)^oC=4.22^oC](https://tex.z-dn.net/?f=T_2-T_1%3D%2825.34-21.12%29%5EoC%3D4.22%5EoC)
Putting values in above equation, we get:
![q=140g\times 4.186J/g^oC\times 4.22^oC=2473.08J=2.473kJ](https://tex.z-dn.net/?f=q%3D140g%5Ctimes%204.186J%2Fg%5EoC%5Ctimes%204.22%5EoC%3D2473.08J%3D2.473kJ)
To calculate the enthalpy change of the reaction, we use the equation:
![\Delta H_{rxn}=\frac{q}{n}](https://tex.z-dn.net/?f=%5CDelta%20H_%7Brxn%7D%3D%5Cfrac%7Bq%7D%7Bn%7D)
where,
q = amount of heat absorbed = 2.473 kJ
n = number of moles of water = 0.0434 moles
= enthalpy change of the reaction
Putting values in above equation, we get:
![\Delta H_{rxn}=\frac{2.473kJ}{0.0434mol}=56.98kJ/mol](https://tex.z-dn.net/?f=%5CDelta%20H_%7Brxn%7D%3D%5Cfrac%7B2.473kJ%7D%7B0.0434mol%7D%3D56.98kJ%2Fmol)
Hence, the amount of heat absorbed by the solution is 56.98 kJ