/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 46 Questions 45-48 refer to the fol... [FREE SOLUTION] | 91Ó°ÊÓ

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Questions 45-48 refer to the following. Inside a calorimeter, 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M}\) hydrocyanic acid (HCN), a weak acid, and 100.0 \(\mathrm{mL}\) of 0.50 \(\mathrm{M}\) sodium hydroxide are mixed. The temperature of the mixture rises from \(21.5^{\circ} \mathrm{C}\) to \(28.5^{\circ} \mathrm{C}\) . The specific heat of the mixture is approximately \(4.2 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C},\) and the density is identical to that of water. What is the approximate amount of heat released during the reaction? \(\begin{array}{ll}{\text { (A) }} & {1.5 \mathrm{kJ}} \\ {\text { (B) }} & {2.9 \mathrm{kJ}} \\ {\text { (C) }} & {5.9 \mathrm{kJ}} \\ {\text { (D) }} & {11.8 \mathrm{kJ}}\end{array}\)

Short Answer

Expert verified
The approximate amount of heat released during the reaction is 5.88kJ. Hence, the closest answer is (C) 5.9 kJ.

Step by step solution

01

Understand the Concept

In a calorimeter, the heat released or absorbed during a chemical reaction is measured. Here, given the temperature change and the density and specific heat of the solution, the heat released can be calculated using q=mc\(\Delta\)T where q is heat, m is mass, c is specific heat capacity and \(\Delta\)T is the change in temperature.
02

Determine the Parameters

The volume of the mixture in the calorimeter is 100.0 mL of HCN + 100.0 mL NaOH = 200.0 mL. Since the density is identical to water, we consider 1 mL = 1 g. So, the mass(m) of the mixture is 200.0 g. The specific heat capacity(c) is provided as 4.2 J/g°C. The change in temperature(\(\Delta\)T) is the final temperature(28.5°C) - initial temperature(21.5°C) = 7.0°C.
03

Calculate Heat q

Substitute the parameters we have determined into the formula: q = mc\(\Delta\)T. The calculation will then look as follows: q = 200.0g * 4.2 J/g°C * 7.0°C = 5880 J.
04

Convert to Kilojoules

As our answer options are given in kilojoules, we need to convert joules to kilojoules by dividing by 1000: q = 5880J/1000 = 5.88 kJ.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Heat Transfer
Heat transfer is a fundamental concept in thermodynamics, especially crucial in calorimetry studies. It refers to the movement of thermal energy from a region of higher temperature to a region of lower temperature until equilibrium is reached. In the context of the calorimeter exercise, when hydrocyanic acid (HCN) reacts with sodium hydroxide (NaOH), heat is either absorbed or released, causing a temperature change.

Understanding heat transfer helps us measure this temperature change to quantify how much heat was involved in the chemical process. Calorimeters are special tools used to capture and measure such heat changes in a controlled environment.

Heat transfer is guided by many factors including:
  • Temperature difference: The greater the difference, the faster the heat transfer.
  • Material properties: Specific heat, conductivity, and mass affect how heat is transferred.
  • Surface area: Greater area can lead to faster heat transfer.
By observing the temperature change in our example, we calculated the heat transfer, showcasing how energy is conserved and transferred as per the First Law of Thermodynamics.
Specific Heat Capacity
Specific heat capacity is a property that tells us how much heat energy is needed to change the temperature of a substance by one degree Celsius. In simpler terms, it measures a material's ability to absorb and store thermal energy. In our calorimetry problem, the specific heat capacity of the mixture is given as 4.2 J/g°C.

This mean that for every gram of the solution, 4.2 joules of energy are required to raise its temperature by 1°C. The specific heat capacity is akin to a substance's thermal signature, helping to predict how it will respond to heat changes.

Knowing the specific heat capacity is essential when calculating the heat transferred during chemical reactions or physical changes.

This property varies between substances due to molecular structure and composition. For example:
  • Water has a high specific heat capacity, which makes it excellent for temperature regulation.
  • Metals typically have lower specific heat capacities, heating and cooling more quickly.
In calorimetry, using the correct specific heat value is vital to obtaining accurate calculations in experimental results.
Chemical Reactions
Chemical reactions are transformations in which substances, known as reactants, change into different substances, called products, involving the breaking and forming of chemical bonds. In a calorimetry context, these reactions often result in the release or absorption of heat, which is what we measure.

In this exercise, the reaction between a weak acid (hydrocyanic acid) and a strong base (sodium hydroxide) is exothermic, meaning it releases heat. The increase in temperature from 21.5°C to 28.5°C recorded in the calorimeter indicates this heat release.

Reactions can be classified by their heat exchanges:
  • Exothermic: Release heat energy, causing temperature increases (as seen in the problem).
  • Endothermic: Absorb heat energy, resulting in temperature decreases.
Studying these heat changes helps in understanding the energetics of reactions including activation energy, and enthalpy, all of which are core topics in high-level chemistry courses such as AP Chemistry.
AP Chemistry
AP Chemistry is an advanced placement course offering high school students the chance to engage in college-level chemistry studies. The course covers a wide range of topics, including the principles of calorimetry, which involves the study of heat involved in chemical reactions and physical changes.

Students learn critical concepts such as:
  • Equations like q = mcΔT, used to calculate heat transfer.
  • Understanding the role of specific heat capacities in substance reactions.
  • Distinguishing between exothermic and endothermic reactions.
This rigorous course prepares students for college-level chemistry by emphasizing scientific inquiry and analysis. Being adept at problems like the calorimetry exercise enhances students' capability to predict and understand energy transformations.

Proficiency in AP Chemistry topics forms a solid foundation that aids students in further exploring the complex interplay of chemical reactions and energy, which are vital for careers in science, technology, engineering, and mathematics (STEM).

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Most popular questions from this chapter

In an experiment 2 moles of \(\mathrm{H}_{2}(g)\) and 1 mole of \(\mathrm{O}_{2}(g)\) were completely reacted, according to the following equation in a sealed container of constant volume and temperature: $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)$$ If the initial pressure in the container before the reaction is denoted as \(P_{i}\) which of the following expressions gives the final pressure, assuming ideal gas behavior? (A) \(P_{i}\) (B) 2\(P_{i}\) (C) \((3 / 2) P_{i}\) (D) \((2 / 3) P_{i}\)

A gas sample with a mass of 10 grams occupies 5.0 liters and exerts a pressure of 2.0 atm at a temperature of \(26^{\circ} \mathrm{C} .\) Which of the following expressions is equal to the molecular mass of the gas? The gas constant, \(R,\) is \(0.08(\mathrm{L} \times \mathrm{atm}) / \mathrm{mol} \times \mathrm{K}\) ). (A) \((0.08)(299) \mathrm{g} / \mathrm{mol}\) (B) \(\frac{(299)(0.50)}{(2.0)(0.08)} \mathrm{g} / \mathrm{mol}\) (C) \(\frac{299}{0.08} \mathrm{g} / \mathrm{mol}\) (D) \((2.0)(0.08) \mathrm{g} / \mathrm{mol}\)

A laboratory technician wishes to create a buffered solution with a pH of 5. Which of the following acids would be the best choice for the buffer? (A) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \quad K_{a}=5.9 \times 10^{-2}\) (B) \(\mathrm{H}_{3} \mathrm{AsO}_{4} \quad K_{a}=5.6 \times 10^{-3}\) (C) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2} \quad K_{a}=1.8 \times 10^{-5}\) (D) \(\mathrm{HOCl}\) \(\quad K_{a}=3.0 \times 10^{-8}\)

Which of the following species is amphoteric? (A) \(\mathrm{H}^{+}\) (B) \(\mathrm{CO}_{3}^{2-}\) (C) \(\mathrm{HCO}_{3}^{-}\) (D) \(\mathrm{H}_{2} \mathrm{CO}_{3}\)

Questions 45-48 refer to the following. Inside a calorimeter, 100.0 \(\mathrm{mL}\) of 1.0 \(\mathrm{M}\) hydrocyanic acid (HCN), a weak acid, and 100.0 \(\mathrm{mL}\) of 0.50 \(\mathrm{M}\) sodium hydroxide are mixed. The temperature of the mixture rises from \(21.5^{\circ} \mathrm{C}\) to \(28.5^{\circ} \mathrm{C}\) . The specific heat of the mixture is approximately \(4.2 \mathrm{J} / \mathrm{g}^{\circ} \mathrm{C},\) and the density is identical to that of water. As \(\Delta T\) increases, what happens to the equilibrium constant and why? (A) The equilibrium constant increases because more products are created. (B) The equilibrium constant increases because the rate of the forward reaction increases. (C) The equilibrium constant decreases because the equilibrium shifts to the left. (D) The value for the equilibrium constant is unaffected by temperature and will not change.

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