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Chapter 6: Problem 60

In a coffee-cup calorimeter, \(100.0 \mathrm{~mL}\) of \(1.0 \mathrm{M} \mathrm{NaOH}\) and \(100.0 \mathrm{~mL}\) of \(1.0 \mathrm{M} \mathrm{HCl}\) are mixed. Both solutions were originally at \(24.6^{\circ} \mathrm{C}\). After the reaction, the final temperature is \(31.3^{\circ} \mathrm{C}\). Assuming that all the solutions have a density of \(1.0 \mathrm{~g} / \mathrm{cm}^{3}\) and a specific heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\), calculate the enthalpy change for the neutralization of \(\mathrm{HCl}\) by \(\mathrm{NaOH}\). Assume that no heat is lost to the surroundings or to the calorimeter.

Short Answer

Expert verified
The enthalpy change for the neutralization of HCl by NaOH is \(56,116 \: J/mol\).

Step by step solution

01

1. Calculate the temperature difference

First, we need to determine the change in temperature during the reaction. To do this, subtract the initial temperature from the final temperature: ΔT = T_final - T_initial = 31.3°C - 24.6°C = 6.7°C
02

2. Calculate the mass of the mixture

To find the mass of the mixture, multiply the volume by the density: mass = volume x density = (100.0 mL HCl + 100.0 mL NaOH) x 1.0 g/cm³ = 200 g
03

3. Calculate the heat released (Q)

Now we will calculate the heat released during the reaction using the formula Q = mcΔT, where m is mass and c is the specific heat capacity. Q = mass x specific heat capacity x ΔT = 200 g x 4.18 J/°C·g x 6.7°C = 5611.6 J
04

4. Calculate the number of moles of HCl and NaOH

Next, we need to determine the number of moles of reactants. Since HCl and NaOH have the same volume and concentration, their mole amounts are equal. moles = concentration x volume = 1.0 mol/L x 0.100 L = 0.100 mol
05

5. Calculate the enthalpy change

Finally, we will find the enthalpy change for the neutralization reaction by dividing the total heat released (Q) by the number of moles of reactants involved in the reaction. Enthalpy change (ΔH) = Q / moles = 5611.6 J / 0.100 mol = 56116 J/mol The enthalpy change for the neutralization of HCl by NaOH is \(56,116 \: J/mol\).

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Most popular questions from this chapter

Combustion reactions involve reacting a substance with oxygen. When compounds containing carbon and hydrogen are combusted, carbon dioxide and water are the products. Using the enthalpies of combustion for \(\mathrm{C}_{4} \mathrm{H}_{4}(-2341 \mathrm{~kJ} / \mathrm{mol}), \mathrm{C}_{4} \mathrm{H}_{8}(-2755 \mathrm{~kJ} / \mathrm{mol})\), and \(\mathrm{H}_{2}(-286 \mathrm{~kJ} / \mathrm{mol})\), calculate \(\Delta H\) for the reaction $$ \mathrm{C}_{4} \mathrm{H}_{4}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{4} \mathrm{H}_{8}(g) $$

In a coffee-cup calorimeter, \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{AgNO}_{3}\) and \(50.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\) are mixed to yield the following reaction: $$ \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \mathrm{AgCl}(s) $$ The two solutions were initially at \(22.60^{\circ} \mathrm{C}\), and the final temperature is \(23.40^{\circ} \mathrm{C}\). Calculate the heat that accompanies this reaction in \(\mathrm{kJ} / \mathrm{mol}\) of \(\mathrm{AgCl}\) formed. Assume that the combined solution has a mass of \(100.0 \mathrm{~g}\) and a specific heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\).

Calculate the internal energy change for each of the following. a. One hundred (100.) joules of work is required to compress a gas. At the same time, the gas releases \(23 \mathrm{~J}\) of heat. b. A piston is compressed from a volume of \(8.30 \mathrm{~L}\) to \(2.80 \mathrm{~L}\) against a constant pressure of \(1.90 \mathrm{~atm} .\) In the process, there is a heat gain by the system of \(350 . \mathrm{J}\). c. A piston expands against \(1.00 \mathrm{~atm}\) of pressure from \(11.2 \mathrm{~L}\) to \(29.1 \mathrm{~L}\). In the process, \(1037 \mathrm{~J}\) of heat is absorbed.

In a coffee-cup calorimeter, \(1.60 \mathrm{~g} \mathrm{NH}_{4} \mathrm{NO}_{3}\) is mixed with \(75.0 \mathrm{~g}\) water at an initial temperature of \(25.00^{\circ} \mathrm{C}\). After dissolution of the salt, the final temperature of the calorimeter contents is \(23.34^{\circ} \mathrm{C}\). Assuming the solution has a heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) and assuming no heat loss to the calorimeter, calculate the enthalpy change for the dissolution of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) in units of \(\mathrm{kJ} / \mathrm{mol}\).

Are the following processes exothermic or endothermic? a. When solid \(\mathrm{KBr}\) is dissolved in water, the solution gets coldel b. Natural gas \(\left(\mathrm{CH}_{4}\right)\) is burned in a furnace. c. When concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is added to water, the solution get very hot. d. Water is boiled in a teakettle.
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