The corrosion (rusting) of iron in oxygen-free water includes the formation of iron(II) hydroxide from iron by the following reaction: Fe(s) + 2 H2O(l) → Fe(OH)2(s) + H2(g). (b) Calculate the number of grams of Fe needed to release enough energy to increase the temperature of 250 mL of water from 22 to 30 °C.

Verified step by step guidance

Step 1: Calculate the amount of heat energy required to raise the temperature of 250 mL of water from 22 °C to 30 °C using the formula q = mcΔT, where m is the mass of water, c is the specific heat capacity of water (4.18 J/g°C), and ΔT is the change in temperature.

Step 2: Convert the volume of water (250 mL) to mass, knowing that the density of water is approximately 1 g/mL, so the mass of water is 250 g.

Step 3: Substitute the values into the formula q = mcΔT to find the heat energy required. Use m = 250 g, c = 4.18 J/g°C, and ΔT = 30°C - 22°C.

Step 4: Determine the enthalpy change (ΔH) for the reaction Fe(s) + 2 H2O(l) → Fe(OH)2(s) + H2(g) from a reliable source or database, as this will be needed to relate the heat energy to the amount of iron reacted.

Step 5: Use the enthalpy change (ΔH) and the heat energy calculated in Step 3 to find the number of moles of Fe required. Then, convert moles of Fe to grams using the molar mass of Fe (55.85 g/mol).

Key Concepts

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

Thermochemistry

Thermochemistry is the study of the heat energy associated with chemical reactions and physical transformations. It involves understanding how energy is absorbed or released during reactions, which is crucial for calculating temperature changes in substances, such as water in this case. The specific heat capacity of water, which is the amount of energy required to raise the temperature of a given mass of water by one degree Celsius, plays a key role in these calculations.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to determine how much of a substance is needed or produced in a reaction based on balanced chemical equations. In this question, stoichiometry will help calculate the mass of iron required to produce a specific amount of energy, which is necessary for heating the water.

Energy Transfer

Energy transfer refers to the movement of energy from one system to another, often in the form of heat. In the context of this question, the energy released from the reaction of iron with water is used to increase the temperature of the water. Understanding the principles of energy transfer, including concepts like enthalpy and heat capacity, is essential for calculating how much iron is needed to achieve the desired temperature change.

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Textbook Question

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C (b) Determine the amount of heat gained by the water. The specific heat of water is 4.184 J/1gK.

A coffee-cup calorimeter of the type shown in Figure 5.18 contains 150.0 g of water at 25.1°C A 121.0-g block of copper metal is heated to 100.4°C by putting it in a beaker of boiling water. The specific heat of Cu(s) is 0.385 J/g-K The Cu is added to the calorimeter, and after a time the contents of the cup reach a constant temperature of 30.1°C (d) What would be the final temperature of the system if all the heat lost by the copper block were absorbed by the water in the calorimeter?

(b) Assuming that there is an uncertainty of 0.002 °C in each temperature reading and that the masses of samples are measured to 0.001 g, what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

We can use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethane: 2 CH4(g) → C2H6(g) + H2(g) Calculate the ΔH° for this reaction using the following thermochemical data: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) ΔH° = -890.3 kJ 2 H2(g) + O2(g) → 2 H2O(l) H° = -571.6 kJ 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(l) ΔH° = -3120.8 kJ

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Textbook Question

From the following data for three prospective fuels, calculate which could provide the most energy per unit mass and per unit volume:

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