The heat of solution of \(\mathrm{KI}(\mathrm{s})\) in water is \(+20.3 \mathrm{kJ} / \mathrm{mol}\) KI. If a quantity of KI is added to sufficient water at \(23.5^{\circ} \mathrm{C}\) in a Styrofoam cup to produce \(150.0 \mathrm{mL}\) of 2.50 M KI, what will be the final temperature? (Assume a density of \(1.30 \mathrm{g} / \mathrm{mL}\) and a specific heat of \(2.7 \mathrm{Jg}^{-1}\) \(\left.^{\circ} \mathrm{C}^{-1} \text {for } 2.50 \mathrm{M} \mathrm{KI} .\right)\)

Short Answer

Expert verified
The final temperature of the solution will be 37.8 °C.

Step by step solution

01

Calculate the moles of \(\mathrm{KI}\)

Firstly, we need to determine the amount of \(\mathrm{KI}\) in moles. To do so, multiply the volume of the solution by its molarity: \(n = V \cdot M\) where \(V = 150 \, mL = 0.150 \, L\) and \(M = 2.5 \, M\). Thus, \(n = 0.150 \, L \cdot 2.5 \, mol/L = 0.375 \, mol\).
02

Calculate the heat of solution Q

The heat of solution of \(\mathrm{KI}\) is given as \(+20.3 \, kJ/mol\). Therefore, the total heat produced when \(\mathrm{KI}\) dissolves can be calculated by multiplying the heat of solution per mole by the number of moles dissolved: \(Q = +20.3 \, kJ/mol \cdot 0.375 \, mol = +7.613 \, kJ\). The positive sign indicates this is an endothermic process, so the solution absorbs heat from its surroundings.
03

Convert Q to J

The value of Q obtained in the previous step should be converted from kJ to J because the specific heat is given in J/g°C. \(Q = +7.613 \, kJ = +7613 \, J\).
04

Calculate the mass of the solution

The mass (m) of the solution can be calculated by multiplying the volume of the solution by its density: \(m = V \cdot d = 150 \, mL \cdot 1.30 \, g/mL = 195 \, g\).
05

Determine \(\Delta T\) (change in temperature)

Use the formula \(q=mc\Delta T\) to find \( \Delta T\', which is \( \Delta T=q/(mc)\). The total heat Q=7613 J, the mass m of the solution is 195 g, and the specific heat c is 2.7 J/g°C. So, \( \Delta T = 7613 J / (195 g \cdot 2.7 J/g°C) = \Delta T = 14.3 °C ).
06

Calculate the final temperature

The final temperature is calculated by summing the initial temperature with the change in temperature: \(T_{final} = T_{initial} + \Delta T = 23.5 °C + 14.3 °C = 37.8 °C\).

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