Ch.5 - Thermochemistry

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.5 - Thermochemistry

Problem 111b

Chapter 5, Problem 111b

(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?

Verified step by step guidance

Step 1: Identify the formula for the heat of combustion. The heat of combustion (q) 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.

Step 2: Determine the variables involved in the calculation. In this problem, the variables are the mass (m), the specific heat capacity (c), and the change in temperature (ΔT).

Step 3: Understand the uncertainties in the measurements. The uncertainty in the temperature reading is ±0.002 °C, and the uncertainty in the mass measurement is ±0.001 g.

Step 4: Use the propagation of uncertainty formula to estimate the uncertainty in the heat of combustion. The formula for propagation of uncertainty in multiplication is: (Δq/q) = (Δm/m) + (Δc/c) + (ΔΔT/ΔT).

Step 5: Calculate the uncertainty in the heat of combustion per mole of caffeine. Convert the uncertainty in q to per mole by considering the molar mass of caffeine and apply the propagation of uncertainty to find the final uncertainty.

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Key Concepts

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

Uncertainty in Measurements

Uncertainty in measurements refers to the doubt that exists about the result of a measurement. It is crucial in experimental science, as it quantifies the range within which the true value is expected to lie. In this context, the uncertainty in temperature readings and mass measurements directly affects the calculated heat of combustion, highlighting the importance of precision in experimental data.

Heat of Combustion

The heat of combustion is the amount of energy released when a substance undergoes complete combustion with oxygen. It is typically expressed in kilojoules per mole (kJ/mol) and is a critical parameter in thermochemistry. Understanding how to calculate this value, including the role of uncertainties in the measurements of temperature and mass, is essential for accurate thermodynamic assessments.

Propagation of Uncertainty

Propagation of uncertainty is a method used to determine the overall uncertainty in a calculated result based on the uncertainties of the individual measurements involved. When multiple measurements are combined in calculations, such as in determining the heat of combustion, the uncertainties must be combined using specific mathematical rules to estimate the total uncertainty in the final result.

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Textbook Question

The Sun supplies about 1.0 kilowatt of energy for each square meter of surface area (1.0 kW/m², where a watt=1 J/s). Plants produce the equivalent of about 0.20 g of sucrose (C12H22O11) per hour per square meter. Assuming that the sucrose is produced as follows, calculate the percentage of sunlight used to produce sucrose. 12 CO2(g) + 11 H2O(l) → C12H22O11 + 12 O2(g) H = 5645 kJ

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Textbook Question

A house is designed to have passive solar energy features. Brickwork incorporated into the interior of the house acts as a heat absorber. Each brick weighs approximately 1.8 kg. The specific heat of the brick is 0.85 J/g•K. How many bricks must be incorporated into the interior of the house to provide the same total heat capacity as 1.7⨉10³ gal of water?

1818

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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.

Potassium superoxide, KO₂, is often used in oxygen masks (such as those used by firefighters) because KO₂ reacts with CO₂ to release molecular oxygen. Experiments indicate that 2 mol of KO₂(s) react with each mole of CO₂(g). (b) Indicate the oxidation number for each atom involved in the reaction in part (a). What elements are being oxidized and reduced?

985

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Textbook Question

Depending on their specific usage, fuels are judged in part on energy released per unit volume and energy released per unit mass. Three prospective fuels are listed in the following table, along with their densities and molar enthalpies of combustion.

a. Rank the three fuels according to their enthalpy produced per gram.

b. Rank them according to their enthalpy produced per cm3:

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