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Chapter 3: Problem 28

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

Short Answer

Expert verified
One mole of \(\mathrm{CO}_{2}\) contains 6.022 x 10^23 molecules, with a molar mass of 44.01 g/mol. It is a linear nonpolar molecule with double covalent bonds between the carbon atom and two oxygen atoms. At standard conditions (0掳C, 1 atm), 1 mole of CO2 occupies approximately 22.4 L and obeys the ideal gas law. CO2 is produced by various processes, such as cellular respiration and combustion of carbon-containing fuels, and plays a significant role in the carbon cycle and Earth's temperature regulation.

Step by step solution

01

1. Definition of a mole

A mole is the unit of measurement for the amount of substance in a system. It is based on the number of atoms, ions, or molecules present in a substance. One mole of any substance contains the same number of entities (atoms, ions, or molecules) as there are in 12 grams of pure carbon-12.
02

2. Molecular formula and structure of CO2

Carbon dioxide (CO2) is a linear nonpolar molecule containing one carbon atom and two oxygen atoms, with the molecular formula \(\mathrm{CO}_{2}\). The carbon atom is located in the middle, bound to both oxygen atoms through double covalent bonds. The bond angle between the oxygen atoms is 180掳, which results in a linear structure and symmetrical charge distribution.
03

3. Molar mass of CO2

To calculate the molar mass of CO2, we need to sum the atomic masses of each element present in the molecule. The atomic mass of carbon is 12.01 u, and the atomic mass of oxygen is 16.00 u. Molar mass of CO2 = (1 x 12.01) + (2 x 16.00) = 44.01 g/mol.
04

4. Avogadro's number

One mole of a substance contains Avogadro's number (N) of entities (atoms, ions, or molecules). Avogadro's number is approximately 6.022 x 10^23 entities per mole. Therefore, 1 mole of CO2 contains approximately 6.022 x 10^23 CO2 molecules.
05

5. Properties under standard conditions

Under standard conditions (0掳C, and 1 atm pressure), CO2 behaves as an ideal gas and obeys the ideal gas law: \(PV = nRT\), where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Using the ideal gas law, we can find the volume occupied by 1 mole of CO2 at standard conditions: \[V = \frac{nRT}{P} = \frac{(1)(0.0821 \frac{\mathrm{L} \cdot \mathrm{atm}}{\mathrm{mol}\cdot\mathrm{K}})(273\mathrm{K})}{1 \mathrm{atm}}\approx 22.4\ \mathrm{L}\].
06

6. Everyday examples and production

CO2 is a ubiquitous gas in our daily lives. It is produced by cellular respiration, combustion of carbon-containing fuels, and other chemical processes. CO2 is an essential component of the carbon cycle and plays a significant role in regulating Earth's temperature due to its greenhouse gas properties. One mole of CO2 could be produced by burning 1.63 grams of glucose or emitting 44.01 liters of car exhaust.

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