A quantity of 1.00 × 10² mL of 0.500 M HCl was mixed with 1.00 × 10² mL of 0.500 M NaOH in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the HCl and NaOH solutions was the same, 22.50°C, and the final temperature of the mixed solution was 25.86°C. Calculate

Question

A quantity of 1.00 × 10² mL of 0.500 M HCl was mixed with 1.00 × 10² mL of 0.500 M NaOH in a constant-pressure calorimeter of negligible heat capacity. The initial temperature of the HCl and NaOH solutions was the same, 22.50°C, and the final temperature of the mixed solution was 25.86°C. Calculate the heat change for the neutralization reaction on a molar basis:

NaOH(aq) + HCl(aq) → NaCl(aq) + [latex]H_{2}O(l)[/latex]

Assume that the densities and specific heats of the solutions are the same as for water (1.00 g/mL and 4.184 J/g · °C, respectively).

Strategy Because the temperature rose, the neutralization reaction is exothermic. How do we calculate the heat absorbed by the combined solution? What is the heat of the reaction? What is the conversion factor for expressing the heat of reaction on a molar basis?

Accepted Answer

Assuming no heat is lost to the surroundings, [latex]q_{sys} = q_{soln} + q_{rxn} = 0, so q_{rxn} = −q_{soln}[/latex], where qsoln is the heat absorbed by the combined solution. Because the density of the solution is 1.00 g/mL, the mass of a 100-mL solution is 100 g. Thus,

[latex]q_{soln} = mcΔt[/latex]

= (1.00 × 10²g + 1.00 × 10²g)(4.184 J/g · °C)(25.86°C − 22.50°C)

= 2.81 × 10³ J

= 2.81 kJ

Because [latex] q_{rxn} = −q_{soln}, q_{rxn} = −2.81 kJ[/latex].

From the molarities given, the number of moles of both HCl and NaOH in 1.00 × 10² mL solution is

[latex]\frac{0.500 mol}{1 L} imes 0.100 L=0.0500 mol [/latex]

Therefore, the heat of neutralization when 1.00 mole of HCl reacts with 1.00 mole of NaOH is

heat of neutralization =[latex]\frac{-2.81 kJ}{0.0500 mol}=-56.2 J/mol[/latex]

Check Is the sign consistent with the nature of the reaction? Under the reaction condition, can the heat change be equated to the enthalpy change?

Question 6.8: A quantity of 1.00 × 10² mL of 0.500 M HCl was mixed with 1....

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