Question

If 2.33 L of propane at 24°C and 67.2 kPa is completely burned in excess oxygen, how many moles of carbon dioxide will be produced?

Short answer

The balanced chemical equation for the combustion of propane (C3H8) with oxygen (O2) is: C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g). Using the Ideal Gas Law, the moles of propane (n) can be calculated as n ≈ 0.0913 moles. From the balanced equation, we determine that for every one mole of propane, we have three moles of carbon dioxide produced. Therefore, the moles of carbon dioxide produced is approximately 0.2739 moles.

Step-by-step solution

Write the balanced chemical equation for propane combustion

The balanced chemical equation for the combustion of propane (C3H8) with oxygen (O2) is: C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(g) This reaction tells us the stoichiometric ratios of the reactants and products involved in propane combustion.

Use the Ideal Gas law to calculate the number of moles of propane

First, we convert the temperature in Celsius to Kelvin: T(K) = T(°C) + 273.15 T(K) = 24°C + 273.15 = 297.15 K Now we use the Ideal Gas Law equation: PV = nRT Where: P = pressure (67.2 kPa) V = volume (2.33 L) n = number of moles of propane R = Ideal gas constant. Note that the value of R changes depending on the pressure used. We'll use the value 8.314 JK/molK and convert the pressure to Pa. T = temperature (297.15 K) We can solve for the moles of propane (n): n = PV / RT First, convert the pressure to Pascal: 67.2 kPa = 67.2 * 1000 = 67200 Pa Then, plug in the given values: n = (67200 Pa)(2.33 L * 10^-3 m^3/L) / (8.314 JK/molK)(297.15 K)

Calculate the moles of propane

After calculating the expression from step 2, we get the moles of propane: n ≈ 0.0913 moles

Use stoichiometry to determine the moles of carbon dioxide produced

From the balanced equation, we know that for every one mole of propane, we have three moles of carbon dioxide produced. So, moles of carbon dioxide = 0.0913 moles of propane * (3 moles of CO2/1 mole of C3H8)

Calculate the moles of carbon dioxide produced

Completing the calculation from step 4, we find the number of moles of carbon dioxide produced: moles of CO2 ≈ 0.2739 moles So, when 2.33 L of propane at 24°C and 67.2 kPa is completely burned in excess oxygen, approximately 0.2739 moles of carbon dioxide will be produced.

Key concepts

Ideal Gas Law

The Ideal Gas Law is an essential principle in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is represented by the equation:
$PV=nRT$.
Here, $P$ represents pressure, $V$ stands for volume, $n$ indicates the number of moles of gas, $R$ is the Ideal gas constant, and $T$ denotes the temperature in Kelvin. This law provides a foundation for understanding how gases behave under different conditions. In the context of the exercise, the Ideal Gas Law was used to calculate the number of moles of propane before it underwent combustion. It is crucial to remember that the value of the Ideal gas constant, $R$, must match the units used for pressure. If pressure is in kilopascals (kPa), then $R$ should have the units $J/(mol\cdot K)$ once the pressure has been converted into Pascals (Pa), as illustrated in the solution steps.
Understanding the Ideal Gas Law can also explain why changes in temperature or pressure impact gas volumes, which can be particularly interesting when considering real-life applications like weather balloons or the behavior of tires in varying climates.

Chemical Equations

Chemical equations are concise representations of chemical reactions, detailing the reactants consumed and the products formed. A balanced chemical equation has an equal number of atoms for each element on both the reactant and product side. The equation for the combustion of propane provided in the solution is a perfect example:
${\text{C}}_3{\text{H}}_8(g)+5{\text{O}}_2(g)\to 3{\text{CO}}_2(g)+4{\text{H}}_2\text{O}(g)$.
This equation follows the law of conservation of mass, indicating that three moles of carbon dioxide and four moles of water are produced for every mole of propane that reacts with five moles of oxygen. It's the stoichiometric ratios in chemical equations that enable us to predict the amounts of reactants needed and products formed, which is fundamental when solving stoichiometry problems. Being able to interpret and balance chemical equations is a critical skill in chemistry that allows students to engage with concepts such as reaction yields, limiting reagents, and theoretical predictions.

Mole Concept

The mole concept is a way to quantify the amount of substance. One mole is defined as the amount of substance containing as many elementary entities (atoms, molecules, ions, etc.) as there are atoms in exactly 12 grams of carbon-12, which is approximately $6.022\times {10}^{23}$ (Avogadro's number). In chemistry, the mole serves as a bridge between the atomic and macroscopic worlds, turning abstract count of atoms into measurable quantities.
When dealing with chemical reactions, as in the propane combustion problem, we use the mole concept to connect the volume of gas (using the Ideal Gas Law) to the amount of substance reacted or produced. The proportional relationship between reactants and products, as outlined in the balanced chemical equation, can only be understood through moles. For instance, knowing that the combustion of propane results in three times as many moles of carbon dioxide requires us to first calculate the moles of propane through the Ideal Gas Law, then apply stoichiometric ratios, as guided in the steps. Grasping the mole concept is vital for successful problem-solving in stoichiometry and other quantitative aspects of chemistry.