Problem 26 - Chemistry An Atoms First Approach

Question

Describe 1 mole of \(\mathrm{CO}_{2}\) in as many ways as you can.

Step-by-Step Solution

Answer

1 mole of \(\mathrm{CO}_{2}\) contains \(6.022\times10^{23}\) molecules, has a molecular composition of \(6.022\times10^{23}\) carbon atoms and \(2\times(6.022\times10^{23})\) oxygen atoms, and has a mass of 44 grams. At STP, it occupies a volume of 22.4 liters with a density of approximately \(1.964\) g/L. Its standard enthalpy of formation is \( -393.5 \) kJ/mol, and it participates in various chemical reactions, such as photosynthesis, where it reacts with water to form glucose and oxygen gas.

Step 1: 1. Define a mole in terms of particles

A mole is the unit of measurement in chemistry that represents \(6.022\times10^{23}\) particles of a substance. In this case, 1 mole of \(\mathrm{CO}_{2}\) contains \(6.022\times10^{23}\) molecules of carbon dioxide.

Step 2: 2. Molecular composition

Each molecule of carbon dioxide (\( \mathrm{CO}_{2} \)) is composed of one carbon atom (C) and two oxygen atoms (O). So, in 1 mole of \(\mathrm{CO}_{2}\), there are \( 6.022\times10^{23} \) carbon atoms and \( 2\times(6.022\times10^{23}) \) oxygen atoms.

Step 3: 3. Molar mass

The molar mass of \(\mathrm{CO}_{2}\) can be calculated using the atomic masses of carbon and oxygen. The atomic mass of carbon is approximately 12 grams per mole, and the atomic mass of oxygen is approximately 16 grams per mole. Thus, the molar mass of \(\mathrm{CO}_{2}\) is \(12 + 2\times16=44 \) grams per mole. So, 1 mole of \(\mathrm{CO}_{2}\) has a mass of 44 grams.

Step 4: 4. Volume at STP

At standard temperature and pressure (STP), which is defined as 0°C (273.15 K) and 1 atmosphere (atm) pressure, the volume of 1 mole of any ideal gas is equal to 22.4 liters. Therefore, at STP, 1 mole of \(\mathrm{CO}_{2}\) occupies a volume of 22.4 liters.

Step 5: 5. Density at STP

The density of a substance can be calculated using the formula: density = mass/volume. At STP, the mass of 1 mole of \(\mathrm{CO}_{2}\) is 44 grams and the volume is 22.4 liters. Therefore, the density of 1 mole of \(\mathrm{CO}_{2}\) at STP is \( \frac{44 \text{g}}{22.4 \text{L}} \approx 1.964 \) g/L.

Step 6: 6. Partial pressure

The partial pressure of \(\mathrm{CO}_{2}\) in a gas mixture can be determined using Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of all the individual gases. If we know the total pressure and the mole fraction (concentration) of \(\mathrm{CO}_{2}\) in the mixture, we can calculate its partial pressure.

Step 7: 7. Energy content

The energy content of \(\mathrm{CO}_{2}\) can be described in terms of its enthalpy of formation, which is the heat released or absorbed when 1 mole of a compound is formed from its constituent elements under standard conditions. The standard enthalpy of formation of \(\mathrm{CO}_{2}\) is \( -393.5 \) kJ/mol, meaning that 393.5 kJ of heat is released when 1 mole of \(\mathrm{CO}_{2}\) is formed from its elements.

Step 8: 8. Chemical reactions involving \(\mathrm{CO}_{2}\)

One mole of \(\mathrm{CO}_{2}\) can also be described in terms of the chemical reactions it participates in. For example, during photosynthesis, 1 mole of \(\mathrm{CO}_{2}\) reacts with 1 mole of water (H₂O) to produce 1 mole of glucose (C₆H₁₂O₆) and 6 moles of oxygen (O₂) gas. In this case, the balanced chemical equation for photosynthesis is: \( \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6} + \mathrm{O}_{2} \).