Answer:
The final temperature of the NaOH solution: <u>T₂ = 37 °C </u>
Explanation:
Given: The enthalpy of NaOH solution:
= – 44.4 kJ/mol,
The specific heat capacity of solution: c = 4.184 J/g.K
Given mass of solute (NaOH): w = 13.9 g, Molar mass of NaOH: m = 40 g/mol
Mass of the solvent: W = 250 g
Initial temperature of the solution: T₁ = 23 °C = 23 + 273 = 296 K (∵ 0°C = 273 K)
Final temperature of the solution: T₂ = ?
<em>The number of moles of NaOH</em> = ![\frac{given\: mass}{molar\: mass} = \frac{13.9\, g}{40\, g/mol} = 0.3475 mol](https://tex.z-dn.net/?f=%5Cfrac%7Bgiven%5C%3A%20mass%7D%7Bmolar%5C%3A%20mass%7D%20%3D%20%5Cfrac%7B13.9%5C%2C%20g%7D%7B40%5C%2C%20g%2Fmol%7D%20%3D%200.3475%20mol)
<u><em>So the amount of heat released (ΔH) by dissolution of 13.9 g NaOH:</em></u>
![\Delta H = \Delta H_{sol} \times n](https://tex.z-dn.net/?f=%5CDelta%20H%20%3D%20%5CDelta%20H_%7Bsol%7D%20%5Ctimes%20n)
![\Rightarrow \Delta H = 15.429 kJ = 15429 J](https://tex.z-dn.net/?f=%5CRightarrow%20%5CDelta%20H%20%3D%2015.429%20kJ%20%3D%2015429%20J)
(∵ 1 kJ = 1000J )
<u><em>Since the specific heat capacity is given by the equation:</em></u>
![c = \frac{\Delta H}{M\times \Delta T}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B%5CDelta%20H%7D%7BM%5Ctimes%20%5CDelta%20T%7D)
Here, M is the total mass of the solution = w + W = 13.9 g + 250 g =263.9 g
<u><em>Thus the increase in the temperature (ΔT) can be calculated as:</em></u>
![\Rightarrow \Delta T = \frac{15429 J}{263.9g \times 4.184J/g.K} = 13.973](https://tex.z-dn.net/?f=%5CRightarrow%20%5CDelta%20T%20%3D%20%5Cfrac%7B15429%20J%7D%7B263.9g%20%5Ctimes%204.184J%2Fg.K%7D%20%3D%2013.973)
![\Rightarrow \Delta T = T_{2} - T_{1} = 13.973](https://tex.z-dn.net/?f=%5CRightarrow%20%5CDelta%20T%20%3D%20T_%7B2%7D%20-%20T_%7B1%7D%20%3D%2013.973)
![\Rightarrow T_{2} = 296K + 13.97 = 309.97K = 309.97 - 273^{\circ }C = 36.97^{\circ }C](https://tex.z-dn.net/?f=%5CRightarrow%20T_%7B2%7D%20%3D%20296K%20%2B%2013.97%20%3D%20309.97K%20%3D%20309.97%20-%20273%5E%7B%5Ccirc%20%7DC%20%3D%2036.97%5E%7B%5Ccirc%20%7DC)
(∵ 0°C = 273 K)
<u>Therefore, the final temperature of the NaOH solution: T₂ = 37 °C </u>