Question

Calculate the number of molecules in each of the following gases at STP: (a) \(0.150 \mathrm{~g}\) of carbon monoxide, \(\mathrm{CO}\) (b) \(2.75 \mathrm{~g}\) of nitrogen monoxide, \(\mathrm{NO}\)

Short answer

(a) CO has approximately \(3.22 \times 10^{21}\) molecules; (b) NO has approximately \(5.51 \times 10^{22}\) molecules.

Step-by-step solution

Understanding the Mole Concept

Moles are used to relate the mass of a substance to its number of constituent particles (such as atoms or molecules). The conversion factor we use is the molar mass of the substance, which is the mass of one mole of a substance and is typically expressed in grams per mole (g/mol).

Determine Molar Mass

To find the molar mass of any compound, we sum the atomic masses of all the atoms in the compound. - For carbon monoxide (CO): The atomic mass of Carbon (C) is approximately 12.01 g/mol, and Oxygen (O) is approximately 16.00 g/mol, giving CO a molar mass of 12.01 + 16.00 = 28.01 g/mol. - For nitrogen monoxide (NO): The atomic mass of Nitrogen (N) is approximately 14.01 g/mol and Oxygen (O) is approximately 16.00 g/mol, giving NO a molar mass of 14.01 + 16.00 = 30.01 g/mol.

Convert Mass to Moles

Convert the given mass of each gas to moles using their respective molar masses: - For CO: \[ \text{Moles of } \text{CO} = \frac{0.150 \text{ g}}{28.01 \text{ g/mol}} \approx 0.00535 \text{ moles} \] - For NO: \[ \text{Moles of } \text{NO} = \frac{2.75 \text{ g}}{30.01 \text{ g/mol}} \approx 0.0916 \text{ moles} \]

Calculate Number of Molecules

To find the total number of molecules, we multiply the number of moles by Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol): - For CO: \[ \text{Number of molecules in } \text{CO} = 0.00535 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 3.22 \times 10^{21} \text{ molecules} \] - For NO: \[ \text{Number of molecules in } \text{NO} = 0.0916 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 5.51 \times 10^{22} \text{ molecules} \]

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry. It represents the mass of one mole of a substance, helping to bridge the gap between the microscopic world of atoms and molecules and our tangible, macroscopic world. You can think of it as the weight of a large pizza that's composed of many smaller slices. To find the molar mass of a compound, simply sum up the atomic masses of each element present in the compound. These atomic masses are usually found on the periodic table under each element's symbol. For example:

• For carbon monoxide (CO), add the atomic masses of carbon (approximately 12.01 g/mol) and oxygen (approximately 16.00 g/mol). This gives CO a molar mass of 28.01 g/mol.
• For nitrogen monoxide (NO), combine the atomic masses of nitrogen (approximately 14.01 g/mol) and oxygen (16.00 g/mol) to obtain a molar mass of 30.01 g/mol.

Molar mass plays a key role in converting grams of a substance to moles. This conversion is often the first step in solving chemistry problems, allowing us to connect weight with the number of particles present.

Avogadro's Number

Avogadro's number is another cornerstone in chemistry, linking the atomic scale with the macroscopic scale. This number, named after scientist Amedeo Avogadro, is approximately \(6.022 \times 10^{23}\), or six hundred sextillion. It indicates the number of atoms or molecules in one mole of any substance. Think of Avogadro's number as a counting unit in chemistry, similar to how a dozen represents 12 items, except this is used for molecules and atoms. By using this number, chemists can determine how many specific particles are in a certain amount of substance.To determine the number of molecules in a given sample, follow these steps:

• Convert the mass of your sample to moles using its molar mass.
• Multiply the number of moles by Avogadro's number to find the total number of molecules.

For instance, with 0.150 grams of carbon monoxide, you calculate its moles and then multiply by Avogadro's number to find approximately \(3.22 \times 10^{21}\) molecules.

STP (Standard Temperature and Pressure)

Standard Temperature and Pressure (STP) is a reference point that helps chemists understand gas properties under specific conditions. At STP, the temperature is set at 0°C (273.15 K) and the pressure is 1 atm (101.3 kPa). These conditions allow scientists to compare and predict gas behaviors more easily. Here's why STP is important:

• Gases behave predictably at STP, making it a useful baseline for scientific calculations.
• At this temperature and pressure, one mole of any ideal gas occupies approximately 22.4 liters of space.
• It provides a consistent standard, removing variables that temperature and pressure can introduce into experiments and calculations.
• When calculations and reactions are reported, STP gives a shared reference for everyone, making data more relatable and understandable among different experiments.

In exercises involving gas calculations, knowing that the conditions assume STP simplifies solving problems such as calculating the number of molecules in a gas sample.