A Peanuts and peanut oil are organic materials and burn in...

A Peanuts and peanut oil are organic materials and burn in air. How many burning peanuts does it take to provide the energy to boil a cup of water $(250 \mathrm{mL} \text { of water }) ?$ To solve this problem, we assume each peanut, with an average mass of $0.73 \mathrm{g}$ is $49 \%$ peanut oil and $21 \%$ starch; the remainder is noncombustible. We further assume peanut oil is palmitic acid, $\mathrm{C}_{16} \mathrm{H}_{32} \mathrm{O}_{2},$ with an enthalpy of formation of $-848.4 \mathrm{kJ} / \mathrm{mol} .$ Starch is a long chain of $C_{6} H_{10} O_{5}$ units, each unit having an enthalpy of formation of $-960 \mathrm{kJ}.$ (IMAGE CANNOT COPY)

Key Concepts

Chemical Energy

Chemical energy refers to the energy stored within the bonds of chemical compounds, which is released during a chemical reaction such as combustion. In this context, burning the organic compounds in peanuts (peanut oil and starch) converts stored chemical energy into heat, which is then used to raise the temperature of water.

Enthalpy of Formation

The enthalpy of formation is the change in energy that occurs when one mole of a compound is formed from its elements in their standard states. It is a measure of the inherent energy within a chemical substance. In the problem, the given enthalpies of formation for palmitic acid (used to model peanut oil) and the starch unit indicate how much energy is contained in these compounds, which is essential for calculating the total energy released during combustion.

Stoichiometry and Percent Composition

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. The percent composition by mass (in this case, the percentages of peanut oil and starch in a peanut) is used to determine the actual amounts of combustible material present. This information is critical for calculating how much energy is generated from burning a peanut, as only certain portions contribute to the energy output.

Heat Transfer and Specific Heat Capacity

Heat transfer is the process by which energy in the form of heat moves from one system to another. The specific heat capacity of a substance, such as water, is the amount of heat required to raise the temperature of a given mass by one degree. To boil water, one must supply enough energy to overcome its heat capacity (and any latent heat if phase change is considered), which in this problem is used to calculate the energy requirement to heat 250 mL of water to its boiling point.

Energy Balance

An energy balance involves equating the energy produced by the combustion of fuel to the energy required to accomplish a task—in this case, boiling a cup of water. By comparing the energy released from burning the combustible contents of a peanut (accounted from enthalpies of formation and stoichiometry) with the thermal energy needed to heat the water, one can determine how many peanuts must be burned to meet the energy demand.

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