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title: "In a coffee-cup calorimeter, a student mixes \\(50.0\\text{ mL}\\) of \\(1.0\\text{ M HCl(aq)}\\) with \\(50.0\\text{ mL}\\) of \\(1.0\\text{ M NaOH(aq)}\\), both initially at \\(22.0\\text{ }^\\circ\\text{C}\\), and observes a maximum temperature increase of \\(\\Delta T_1\\).  In a second trial, the student mixes \\(50.0\\text{ mL}\\) of \\(1.0\\text{ M HCl(aq)}\\) with \\(100.0\\text{ mL}\\) of \\(1.0\\text{ M NaOH(aq)}\\), both initially at \\(22.0\\text{ }^\\circ\\text{C}\\), and observes a maximum temperature increase of \\(\\Delta T_2\\).  Assuming negligible heat exchange with the calorimeter and surroundings, and that the densities and specific heat capacities of all solutions are equal to those of pure water, which of the following correctly compares \\(\\Delta T_2\\) to \\(\\Delta T_1\\) and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/123677/"
date_modified: "2026-09-28T12:01:57+00:00"
---

# In a coffee-cup calorimeter, a student mixes \(50.0\text{ mL}\) of \(1.0\text{ M HCl(aq)}\) with \(50.0\text{ mL}\) of \(1.0\text{ M NaOH(aq)}\), both initially at \(22.0\text{ }^\circ\text{C}\), and observes a maximum temperature increase of \(\Delta T_1\).

In a second trial, the student mixes \(50.0\text{ mL}\) of \(1.0\text{ M HCl(aq)}\) with \(100.0\text{ mL}\) of \(1.0\text{ M NaOH(aq)}\), both initially at \(22.0\text{ }^\circ\text{C}\), and observes a maximum temperature increase of \(\Delta T_2\).

Assuming negligible heat exchange with the calorimeter and surroundings, and that the densities and specific heat capacities of all solutions are equal to those of pure water, which of the following correctly compares \(\Delta T_2\) to \(\Delta T_1\) and provides the correct justification?

In a coffee-cup calorimeter, a student mixes \(50.0\text{ mL}\) of \(1.0\text{ M HCl(aq)}\) with \(50.0\text{ mL}\) of \(1.0\text{ M NaOH(aq)}\), both initially at \(22.0\text{ }^\circ\text{C}\), and observes a maximum temperature increase of \(\Delta T_1\).

In a second trial, the student mixes \(50.0\text{ mL}\) of \(1.0\text{ M HCl(aq)}\) with \(100.0\text{ mL}\) of \(1.0\text{ M NaOH(aq)}\), both initially at \(22.0\text{ }^\circ\text{C}\), and observes a maximum temperature increase of \(\Delta T_2\).

Assuming negligible heat exchange with the calorimeter and surroundings, and that the densities and specific heat capacities of all solutions are equal to those of pure water, which of the following correctly compares \(\Delta T_2\) to \(\Delta T_1\) and provides the correct justification?

- **A.** \(\Delta T_2 < \Delta T_1\), because the same amount of heat is released since \(\text{HCl}\) is the limiting reactant, but the heat is absorbed by a larger total mass of solution.
- **B.** \(\Delta T_2 < \Delta T_1\), because the excess \(\text{NaOH(aq)}\) undergoes an endothermic dilution process that absorbs heat from the neutralization reaction.
- **C.** \(\Delta T_2 > \Delta T_1\), because the greater number of moles of \(\text{NaOH}\) present allows more neutralization to take place, releasing a greater quantity of heat.
- **D.** \(\Delta T_2 > \Delta T_1\), because the larger total volume of solution has a greater heat capacity, enabling it to absorb more energy and achieve a higher final temperature.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123677/*