Question

A binary compound between an unknown element \(\mathrm{E}\) and hydrogen contains \(91.27 \%\) E and \(8.73 \%\) H by mass. If the formula of the compound is \(\mathrm{E}_{3} \mathrm{H}_{8},\) calculate the atomic mass of E.

Short answer

The atomic mass of the unknown element E in the binary compound E3H8, containing \(91.27\%\) E and \(8.73\%\) H by mass, is approximately \(27.84 \, g/mol\).

Step-by-step solution

Calculate the mass of hydrogen in the compound

Since we know that the mass percentage of hydrogen in the compound is \(8.73 \%\), let's assume we have \(100 \, g\) of the compound, so there will be \(8.73 \, g\) of hydrogen.

Calculate the mass of the unknown element E in the compound

Similarly, we know that the mass percentage of E in the compound is \(91.27 \%\), we can calculate the mass of E in \(100 \, g\) of the compound as \(91.27 \, g\).

Calculate the moles of hydrogen in the compound

To find the moles of hydrogen in the compound, we can use the formula: Moles = mass of the element / atomic mass of the element For hydrogen, the atomic mass is approximately \(1 \, g/mol\). Therefore, the moles of hydrogen in the compound are: Moles = \( \frac{8.73 \, g}{1 \, g/mol} = 8.73 \, mol \)

Calculate the moles of E in the compound

Since we know the formula of the compound is E3H8, the mole ratio of E to H is 3:8. We can use this ratio to find the moles of E in the compound. Moles of E = \( \frac{3}{8} \: \times \: 8.73 \, mol \) Moles of E = \( 3.27375 \, mol \)

Calculate the atomic mass of E

Now that we have the moles of E and its mass in the compound, we can calculate the atomic mass of E using the formula: Atomic mass of E = mass of the element / moles of the element Atomic mass of E = \( \frac{91.27 \, g}{3.27375 \, mol} = 27.84 \, g/mol \) Thus, the atomic mass of the unknown element E is approximately \( 27.84 \, g/mol \).

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry used to measure the amount of substance. It reflects the idea that atoms, molecules, and ions are counted not by their number, but by how much they weigh in bulk. This is due to their incredibly small size. When chemists say "one mole" of a substance, they mean Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles, whether those are atoms, molecules, or ions.

This concept is vital for calculating expressions like stoichiometric amounts in chemical reactions. It allows us to relate masses of substances via their chemical equations. In problems involving composition like the one above, moles allow us to translate between masses and molecule counts, crucial for determining the ratios and formula units. A solid understanding of moles leads to seamless functioning in advanced chemical calculations.

Chemical Formula

Chemical formulas are symbolic representations that specify the types and numbers of atoms in a compound. They communicate important information regarding the proportions by which those elements combine. For example, in the exercise's compound \(\text{E}_3\text{H}_8\), the subscripts tell us that there are three atoms of element \(E\) for every eight atoms of hydrogen (\(H\)).

These formulas are determined by the need for compound stability and neutral charge, balancing out the positive and negative charges of atoms involved. Understanding how to interpret and use chemical formulas is crucial for identifying compounds and communicating their properties. Chemical formulas also lead directly to understanding stoichiometry and calculating molecular weights.

Mass Percentage

Mass percentage is a way of expressing the concentration of an element within a compound or mixture. It indicates how much of the total mass of a sample is attributable to a particular component, expressed as a percentage. In the exercise above, we have a compound with mass percentages of \(91.27\%\) for \(E\) and \(8.73\%\) for hydrogen (\(H\)).

This is calculated using the formula: \[ \text{Mass percentage} = \left( \frac{\text{mass of the element}}{\text{total mass of compound}} \right) \times 100 \% \]

Mass percentage is useful for determining the empirical formula and analyzing the composition of compounds. These percentages provide insight into how much of a compound's mass is made up by each of its constituent elements. This is especially helpful in fields ranging from chemical manufacturing to pharmacology, where precision in composition is paramount.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in chemical reactions. By using stoichiometry, we are able to predict the amounts of substances consumed and produced. It involves using balanced chemical equations to calculate mass, moles, and volumes amongst other quantities.

The stoichiometric process relies heavily on the mole concept and chemical formulas. It often begins with determining moles from the given mass (utilizing atomic and molar masses) and applying the mole ratio, derived from the balanced equation, to predict the mass or volume of other substances involved.

For the exercise provided, stoichiometry, in coordination with mole relationships, is crucial. Through stoichiometry, you can ease the complexity of interactions in chemistry, ensuring precise and correct calculations of quantities necessary for scientific research, industrial processes, and day-to-day applications.