Question

One chemical substance in natural gas is a compound called methane. Its molecules are composed of carbon and hydrogen, and each molecule contains four atoms of hydrogen and one atom of carbon. In this compound, \(0.33597 \mathrm{~g}\) of hydrogen is combined with \(1.0000 \mathrm{~g}\) of carbon-12. Use this information to calculate the atomic mass of the element hydrogen.

Short answer

The atomic mass of hydrogen is approximately 1.0079 g/mol.

Step-by-step solution

Determine the Ratio of Hydrogen to Carbon

First, note that the amount of hydrogen is given as 0.33597 g and the amount of carbon is 1.0000 g in the compound methane. We will use these masses to find the ratio of the masses of hydrogen to carbon.

Calculate the Number of Moles of Carbon

Using the molar mass of carbon-12, which is precisely 12.000 g/mol, calculate the number of moles of carbon in the 1.0000 g sample. The number of moles is found by dividing the mass of the sample by the molar mass of carbon: moles of carbon = mass of carbon / molar mass of carbon.

Calculate the Number of Moles of Hydrogen

Assuming the atomic mass of hydrogen is the value we have to find, let's call it 'H'. From the stoichiometry of methane which is CH4 (one carbon atom to four hydrogen atoms), every mole of carbon will bond with 4 moles of hydrogen. Therefore, the number of moles of hydrogen will be 4 times the number of moles of carbon.

Deduce the Atomic Mass of Hydrogen

We know that the mass is the product of the number of moles and the molar mass (atomic mass in this case for hydrogen). So, we use the equation mass of hydrogen = moles of hydrogen × atomic mass of hydrogen. Insert the known values and solve for the atomic mass of hydrogen.

Solve for the Atomic Mass of Hydrogen

Finally, rearrange the equation from Step 4 to isolate the atomic mass of hydrogen (H) and calculate its value using the given mass of hydrogen, the calculated number of moles of hydrogen, and the known stoichiometric ratios.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is the method used to calculate the amounts of substances that are consumed and produced in a given chemical reaction. A fundamental concept in stoichiometry is the mole ratio, which is derived from the balanced chemical equation for the reaction.

In the context of the given exercise, stoichiometry is used to understand the proportions of hydrogen to carbon in methane (CH₄). Since methane has a fixed ratio of one carbon atom to four hydrogen atoms, we know that for each mole of carbon, there will be four moles of hydrogen. Applying stoichiometry, we can then relate these mole ratios to the mass of each element in the compound, which is the key to finding the atomic mass of hydrogen.

Molar Mass

Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a physical property that is a combination of the atomic masses of all the atoms in a formula unit of a compound or element, as found on the periodic table.

For example, the molar mass of carbon-12, which is used as the standard for carbon, is exactly 12.000 g/mol. This allows us to convert between mass and moles of carbon in the exercise. Understanding molar mass is essential for solving the problem because it enables us to find the number of moles of carbon, which is a necessary step in calculating the atomic mass of hydrogen.

Chemical Composition

Chemical composition refers to the identity and ratio of the elements that make up a substance. Each substance has a unique composition that determines its chemical properties. The composition is often represented by a chemical formula, such as CH₄ for methane, which indicates that each molecule contains one carbon and four hydrogen atoms.

In our exercise, methane's chemical composition guides us to understand the stoichiometry of the compound, which in turn helps us to calculate the atomic mass of hydrogen. By knowing the composition and the mass of hydrogen that combines with carbon in methane, we can deduce the mass of a single hydrogen atom when combined in a known ratio to a mass of carbon. This ultimately leads to an accurate calculation of hydrogen's atomic mass.