Question

Calculate the number of molecules present in each of the following samples. a. 6.37 mol of carbon monoxide b. 6.37 g of carbon monoxide c. \(2.62 \times 10^{-6} \mathrm{g}\) of water d. \(2.62 \times 10^{-6}\) mol of water e. \(5.23 \mathrm{g}\) of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\)

Short answer

The number of molecules present in each of the samples is as follows: a. \(3.83 \times 10^{24}\) molecules of carbon monoxide b. \(1.37 \times 10^{23}\) molecules of carbon monoxide c. \(8.73 \times 10^{16}\) molecules of water d. \(1.58 \times 10^{18}\) molecules of water e. \(4.03 \times 10^{22}\) molecules of benzene

Step-by-step solution

a. Calculating the number of molecules in 6.37 mol of carbon monoxide

We are given the number of moles directly: 6.37 mol of carbon monoxide. To determine the number of molecules in this sample, we simply use the formula: Number of molecules = Number of moles \(\times\) Avogadro's number Number of molecules = \(6.37 \times 6.022 \times 10^{23}\) Number of molecules = \(3.83 \times 10^{24}\) molecules of carbon monoxide

b. Calculating the number of molecules in 6.37 g of carbon monoxide

First, let's find the molar mass of carbon monoxide. The molar mass of carbon (C) is 12.01 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol. Then, the molar mass of carbon monoxide (CO) is: Molar mass of CO = 12.01 g/mol (C) + 16.00 g/mol (O) = 28.01 g/mol Now, we need to calculate the number of moles: Number of moles = Mass of the substance / Molar mass Number of moles = 6.37 g / 28.01 g/mol = 0.227 mol Now, calculate the number of molecules: Number of molecules = 0.227 mol × 6.022 ×10^23 molecules/mol = \(1.37 \times 10^{23}\) molecules of carbon monoxide

c. Calculating the number of molecules in \(2.62 \times 10^{-6} \mathrm{g}\) of water

First, we need to find the molar mass of water (H₂O). The molar mass of hydrogen (H) is 1.01 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol. The molar mass of water is: Molar mass of H₂O = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol Now, calculate the number of moles: Number of moles = \( \frac{2.62 \times 10^{-6} g}{18.02 g/mol} = 1.45 \times 10^{-7} mol\) Now, calculate the number of molecules: Number of molecules = \(1.45 \times 10^{-7} mol \times 6.022 \times 10^{23} molecules/mol = 8.73 \times 10^{16}\) molecules of water

d. Calculating the number of molecules in \(2.62 \times 10^{-6}\) mol of water

We are given the number of moles directly: \(2.62 \times 10^{-6}\) mol of water. To determine the number of molecules in this sample, we use the formula: Number of molecules = Number of moles × Avogadro's number Number of molecules = \(2.62 \times 10^{-6} mol \times 6.022 \times 10^{23} molecules/mol = 1.58 \times 10^{18}\) molecules of water

e. Calculating the number of molecules in 5.23 g of benzene, C₆H₆

First, we need to find the molar mass of benzene (C₆H₆). The molar mass of carbon (C) is 12.01 g/mol, and the molar mass of hydrogen (H) is 1.01 g/mol. The molar mass of benzene is: Molar mass of C₆H₆ = 6(12.01 g/mol) + 6(1.01 g/mol) = 78.12 g/mol Now, calculate the number of moles: Number of moles = 5.23 g / 78.12 g/mol = 0.067 mol Now, calculate the number of molecules: Number of molecules = 0.067 mol × 6.022 × 10^23 molecules/mol = \(4.03 \times 10^{22}\) molecules of benzene

Key concepts

Avogadro's Number

One of the most fundamental constants in chemistry is Avogadro's number, which is central to understanding the composition of substances at the molecular level. Named after the Italian scientist Amedeo Avogadro, this number is defined as the amount of entities, such as atoms, ions, or molecules, in one mole of any substance.

Avogadro's number is numerically equal to approximately 6.022 x 10^23 entities per mole. It's akin to having a massive sack of identical items, where instead of counting each one, you weigh the sack to determine how many you have based on a known conversion factor. In the context of chemistry, when working with moles of a substance, you're dealing with huge numbers of microscopic entities that are impractical to count individually.

Using Avogadro's number, chemists can bridge the gap between the macroscopic quantities we measure in the lab (like grams or liters) and the microscopic number of atoms or molecules in those quantities. This facilitates the practical use of chemical equations and stoichiometry in predicting the outcomes of reactions and the amounts of reactants required or products formed.

Molar Mass

The molar mass of a substance is the mass in grams of one mole of that substance. It is essentially the 'weight' of one mole, and it is a crucial conversion factor in chemistry for translating between the mass of a sample and the number of moles contained in that sample.

The molar mass is typically expressed in units of grams per mole (g/mol) and is calculated by summing the atomic masses of all the atoms in a molecule. For elements, the molar mass is the same number as the atomic mass found on the periodic table but is considered in grams per mole rather than atomic mass units (amu).

Understanding molar mass is vital because it allows chemists to measure out specific amounts of substances. To perform a calculation, you divide the mass of your sample by its molar mass to find the number of moles. This step is particularly important in chemical reactions where the proportions of reactants need to be precise for the reaction to proceed optimally.

Moles to Molecules Conversion

Converting moles to molecules is a two-step process that involves first understanding the molar mass of the substance and then using Avogadro's number. This conversion is necessary when you need to find out how many molecules are present in a given amount of a substance, which is a common requirement in chemical calculations.

To perform this conversion, you begin by finding out the number of moles of the substance you have. If the amount is presented in grams, you divide it by the molar mass of the substance to calculate the moles. Once you have the number of moles, you multiply it by Avogadro's number to determine the number of molecules.

The formula can be represented as: Number of molecules = (Mass of the substance / Molar mass) x Avogadro's number. This basic computation is a foundational element in stoichiometry, which is the area of chemistry that pertains to the relative quantities of reactants and products in chemical reactions.