Ch.9 - Thermochemistry: Chemical Energy

Problem 7

Chapter 9, Problem 7

How much heat is required to raise a 50.0 g piece of iron from 25 °C to its melting point of 1538 °C? The specific heat capacity for iron is 0.451 J/g•°C. (a) 34.1 kJ (b) 168 kJ (c) 12.1 kJ (d) 6.78 kJ

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Identify the given values: mass of iron (m) = 50.0 g, initial temperature (T_initial) = 25 °C, final temperature (T_final) = 1538 °C, and specific heat capacity of iron (c) = 0.451 J/g•°C.

Understand the formula for heat transfer, which is Q = m * c * ΔT, where Q is the heat required, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Calculate the change in temperature (ΔT) by subtracting the initial temperature from the final temperature: ΔT = T_final - T_initial.

Substitute the values into the heat transfer formula: Q = 50.0 g * 0.451 J/g•°C * (1538 °C - 25 °C).

Convert the result from joules to kilojoules by dividing by 1000, as 1 kJ = 1000 J.

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Key Concepts

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

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. It is a material-specific property that indicates how much energy is needed to change the temperature of a substance, which is crucial for calculating heat transfer in thermal processes.

Heat Transfer Calculation

The heat transfer (q) required to change the temperature of a substance can be calculated using the formula q = m × c × ΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. This formula allows us to quantify the energy needed for temperature changes in various materials.

Phase Change and Melting Point

The melting point is the temperature at which a solid becomes a liquid. In this context, understanding the melting point of iron (1538 °C) is essential, as it indicates the temperature to which the iron must be heated. The energy required to reach this temperature from an initial state is calculated using the specific heat capacity.

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Related Practice

Textbook Question

Several processes are given in the table and labeled as endo- thermic or exothermic and given a sign for ∆H°. Which process is labeled with the correct sign of ∆H° and correct classification as endothermic or exothermic? (LO 9.8) Process (b) Methane, the main component of natural gas, is burned to produce a flame on a stovetop.

A 25.0 g piece of granite at 100.0°C was added to 100.0 g of water of 25.0°C, and the temperature rose to 28.4°C. What is the specific heat capacity of the granite? (The specific heat capacity for water is 4.18 J/(g•°C).) (LO 9.10) (a) 0.563 J/(g•°C) (b) 1.53 J/(g•°C) (c) 0.992 J/(g•°C) (d) 0.794 J/(g•°C)

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Textbook Question

When 12.5 g of NH4NO3 is dissolved in 150.0 g of water of 25.0 °C in a coffee cup calorimeter, the final temperature of the solution of 19.7 °C. Assume that the specific heat of the solution is the same as that of water, 4.18 J/(g•°C). What is the ΔH per mol of NH4NO3? (LO 9.10) NH4NO3 (s) → NH4+ (aq) + NO3−(aq) ΔH = ? (a) +3.60 kJ (b) +23.0 kJ (c) +21.3 kJ (d) −3.60 kJ

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Textbook Question

Calculate the enthalpy change for the reaction C(s) + 2 H2(g) → CH4(g) ΔH = ? Given the enthalpy values for the following reactions CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) ΔH = −890.4 kJ C(s) + O2(g) → CO2(g) ΔH = −393.5 kJ H2(g) + 1/2 O2(g) → H2O (g) ΔH = −285.8 kJ (a) −1569.7 kJ (b) +211.1 kJ (c) −1855.5 kJ (d) −74.7 kJ

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