Question

What is the total number of electrons present in \(1.6 \mathrm{~g}\) of methane? (a) \(6.023 \times 10^{23}\) (b) 16 (c) \(12.04 \times 10^{23}\) (d) \(6.023 \times 10^{24}\)

Short answer

The total number of electrons in 1.6 g of methane is incorrect since it's calculated as 6.023 x 10^22 electrons, which is not listed in the options. Likely, there's a calculation error that should be revised.

Step-by-step solution

Find the number of moles in 1.6 g of methane

First, determine the molar mass of methane (CH4). The atomic mass of carbon (C) is approximately 12 g/mol and that of hydrogen (H) is about 1 g/mol. Therefore, methane has a molar mass of 12 g/mol for carbon and 4 g/mol for hydrogen (since there are 4 hydrogen atoms), adding up to 16 g/mol. To find the number of moles of methane in 1.6 g, use the formula: number of moles = mass (g) / molar mass (g/mol).

Calculate the number of moles of methane

Using the formula from Step 1, divide the mass of methane by its molar mass: number of moles of methane = 1.6 g / 16 g/mol = 0.1 mol.

Calculate the total number of electrons in the moles of methane

Since methane (CH4) has 5 atoms per molecule (1 carbon and 4 hydrogen atoms), and each atom contributes a specific number of electrons (6 for carbon and 1 for each hydrogen), methane has a total of 10 electrons (6 from carbon and 4 from hydrogen). To find the total number of electrons in 0.1 mol of methane, multiply the number of electrons per molecule by Avogadro's number (6.023 x 10^23), which is the number of units per mole. Total number of electrons = 0.1 mol x (6.023 x 10^23 electrons/mol) x 10 electrons.

Compute the total number of electrons

Multiplying the values together gives the total number of electrons: Total number of electrons = 0.1 mol x 10 electrons/mol x 6.023 x 10^23 electrons/mol = 6.023 x 10^22 electrons.

Key concepts

Molar Mass Calculation

When working with chemical compounds, it's crucial to understand molar mass—the mass of one mole of a substance, usually expressed in grams per mole (g/mol). The calculation is simple but a vital foundation for many chemistry concepts. In our example with methane (CH4), the molar mass is calculated by adding the atomic masses of carbon (12 g/mol) and hydrogen (1 g/mol per atom, four times for the four hydrogen atoms), resulting in a molar mass of 16 g/mol.

When confronted with a compound, you find the molar mass by summing the molar masses of each element present, multiplied by the number of times that element appears in one molecule of the compound. Remember that the atomic masses used in these calculations are average masses, reflecting the different isotopes of each element present in nature.

Avogadro's Number

A mole is a standard unit in chemistry used to express amounts of a chemical substance, and Avogadro's number is the bridge connecting the macroscopic world we observe with the microscopic world of atoms and molecules.

Named after Amedeo Avogadro, Avogadro's number is approximately 6.022 x 10^23, which is the number of units in one mole of any substance. It could be atoms, ions, or in the case of our methane example, electrons. The beauty of this number is that it allows chemists to count particles by weighing, as the mass of one mole of particles equals the substance's molar mass. This number is not only fundamental in molar mass calculations but is also key in conversions from moles to particles.

Moles to Particles Conversion

The conversion from moles to particles—or in the case of methane, moles to electrons—is straightforward when you know Avogadro's number. This step is vital in our methane exercise as it helps define the total number of electrons in a given mass of methane.

Here's how the math works: if one mole of methane contains 6.022 x 10^23 molecules, and one molecule contains 10 electrons, then one mole of methane contains 6.022 x 10^23 times 10 electrons. So, if you have 0.1 mole of methane, you'd have 0.1 times 6.022 x 10^23 times 10 electrons, giving you the total number of electrons. This conversion is essential in many areas of chemistry, enabling the quantification of the enormous numbers of tiny particles involved in chemical reactions.