Ch.9 - Thermochemistry: Chemical Energy

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.9 - Thermochemistry: Chemical Energy

Problem 153c

Chapter 9, Problem 153c

(c) Assume that a chunk of potassium weighing 7.55 g is dropped into 400.0 g of water at 25.0 °C. What is the final temperature of the water if all the heat released is used to warm the water?

Verified step by step guidance

Calculate the moles of potassium (K) using its molar mass. The molar mass of K is approximately 39.10 g/mol. Use the formula: \( \text{moles of K} = \frac{\text{mass of K}}{\text{molar mass of K}} \).

Write the balanced chemical equation for the reaction of potassium with water: \( 2\text{K} + 2\text{H}_2\text{O} \rightarrow 2\text{KOH} + \text{H}_2 \). This reaction is exothermic, meaning it releases heat.

Determine the amount of heat released by the reaction. Use the enthalpy change for the reaction, which can be found in a reference source. Multiply the moles of K by the enthalpy change per mole of K to find the total heat released.

Use the specific heat capacity formula to find the change in temperature of the water. The formula is \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat absorbed by the water, \( m \) is the mass of the water, \( c \) is the specific heat capacity of water (4.18 J/g°C), and \( \Delta T \) is the change in temperature.

Solve for the final temperature of the water by rearranging the formula to \( \Delta T = \frac{q}{m \cdot c} \) and adding the initial temperature of the water to \( \Delta T \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Heat Transfer

Heat transfer is the process by which thermal energy moves from one object or substance to another due to a temperature difference. In this scenario, the heat released by the potassium as it reacts with water will be absorbed by the water, leading to an increase in its temperature. Understanding this concept is crucial for calculating the final temperature of the water.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. Each substance has a unique specific heat capacity, which influences how much its temperature will change when heat is added or removed. For water, the specific heat capacity is approximately 4.18 J/g°C, which is essential for determining how much the temperature of the water will increase in response to the heat from the potassium.

Calorimetry

Calorimetry is the science of measuring the heat of chemical reactions or physical changes. In this problem, calorimetry principles can be applied to calculate the final temperature of the water by equating the heat lost by the potassium to the heat gained by the water. This involves using the formula Q = mcΔT, where Q is the heat exchanged, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

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Related Practice

Textbook Question

Acid spills are often neutralized with sodium carbonate or sodium hydrogen carbonate. For neutralization of acetic acid, the unbalanced equations are

(1) CH₃CO₂H(l) + Na₂CO₃(s) → CH₃CO₂Na(aq) + CO₂(g) + H₂O(l)

(2) CH₃CO₂H(l) + NaHCO₃(s) → CH₃CO₂Na(aq) + CO₂(g) + H₂O(l)

(a) Balance both equations.

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Textbook Question

Acid spills are often neutralized with sodium carbonate or sodium hydrogen carbonate. For neutralization of acetic acid, the unbalanced equations are

(1) CH₃CO₂H(l) + Na₂CO₃(s) → CH₃CO₂Na(aq) + CO₂(g) + H₂O(l)

(2) CH₃CO₂H(l) + NaHCO₃(s) → CH₃CO₂Na(aq) + CO₂(g) + H₂O(l)

(b) How many kilograms of each substance is needed to neutralize a 1.000-gallon spill of pure acetic acid (density = 1.049 g/mL)?

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Textbook Question

(d) What is the molarity of the KOH solution prepared in part (c), and how many milliliters of 0.554 M H2SO4 are required to neutralize it?

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Textbook Question

Reaction of gaseous fluorine with compound X yields a single product Y, whose mass percent composition is 61.7% F and 38.3% Cl. (a) What is a probable molecular formula for product Y, and what is a probable formula for X?

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Textbook Question

(b) Use the data in Appendix B to calculate ΔH° for the reaction of potassium metal with water.

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