91Ó°ÊÓ

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It’s expressed as \(PV = nRT\), where \(P\) stands for pressure, \(V\) for volume, \(n\) for the number of moles, \(R\) is the ideal gas constant, and \(T\) represents the temperature in kelvins.
Understanding this law allows us to predict how changes in one property of a gas affect the others, provided the gas behaves ideally. Ideal behavior assumes that gas molecules do not interact and occupy no space; real gases approximate this under low pressure and high temperature.
In our problem, we used the Ideal Gas Law to relate the change in pressure to the change in moles of gases. The pressure increased by 17% because the number of moles in the cylinder increased after the reactions.

Balanced chemical equations are essential in stoichiometry as they ensure that atoms are conserved in a reaction. The coefficients in a balanced equation show the ratio of moles needed for reactants and products.
For this problem, it was crucial to balance the equations for the conversion of carbon (graphite) to carbon monoxide (\(CO\)) and carbon dioxide (\(CO_2\)):

• \(C + \frac{1}{2}O_2 \rightarrow CO\)
• \(C + O_2 \rightarrow CO_2\)

These equations help us understand that it requires different amounts of oxygen to produce \(CO\) and \(CO_2\). Balancing these reactions allows us to calculate the moles of leftover reactants and generated products.

Mole fraction is a way of expressing the ratio of moles of a particular component to the total moles of a mixture. It is denoted as \(X\), such that the sum of mole fractions in a mixture always equals 1.
In this exercise, once we determined the moles of the products \(CO\) and \(CO_2\), and the remaining \(O_2\), we calculated their specific mole fractions as follows:

• Mole fraction of \(CO\) = \(\frac{1.7}{5.85}\)
• Mole fraction of \(CO_2\) = \(\frac{3.3}{5.85}\)
• Mole fraction of \(O_2\) = \(\frac{0.85}{5.85}\)

Mole fractions help in understanding the composition of the final gaseous mixture formed post-reaction.

Combustion reactions involve the burning of a substance in the presence of oxygen to produce energy, often yielding heat and light. They are generally highly exothermic.
In our problem, graphite and oxygen undergo combustion when ignited, forming mixtures of \(CO\) and \(CO_2\). The balanced equations for these reactions reflect two possible stoichiometric pathways for the carbon: partial oxidation to \(CO\) or complete oxidation to \(CO_2\).
This dual-path process explains why we have a mixture of \(CO\) and \(CO_2\) as products. Understanding combustion reactions requires knowledge of different potential reaction pathways and the energy changes associated with them.