The enthalpy of solution of sodium hydroxide is –44.4 kj/mol. when a 13.9-g sample of naoh dissolves in 250.0 g of water 23.0 °c in a coffee-cup calorimeter, what is the final temperature of the solution assuming no heat is lost to the surroundings. the solution has the same specific heat of 4.184 j/g-k.

The final temperature of the NaOH solution: T₂ = 37 °C  

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 = ?

The number of moles of NaOH =

So the amount of heat released (ΔH) by dissolution of 13.9 g NaOH:

(∵ 1 kJ = 1000J )

Since the specific heat capacity is given by the equation:

Here,  M is the total mass of the solution = w + W = 13.9 g + 250 g =263.9 g

Thus the increase in the temperature (ΔT) can be calculated as:

(∵ 0°C = 273 K)

Therefore, the final temperature of the NaOH solution: T₂ = 37 °C  

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