Question

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

Short answer

The atomic mass of Element E is approximately 27.87 amu.

Step-by-step solution

Calculate the total mass of Hydrogen in the compound

Since the formula of the compound is E3H8, it means there are 8 hydrogen atoms in the compound. We know that the atomic mass of hydrogen is approximately 1 amu (atomic mass unit). Therefore, the total mass of hydrogen in the compound is: Total mass of hydrogen = (8 atoms of hydrogen) * (1 amu/atom of hydrogen) = 8 amu

Calculate the total mass of the compound

We are given the percentage composition of the compound. Since hydrogen represents 8.73% of the compound, the total mass of the compound can be expressed as: Total mass of compound = (Total mass of hydrogen) / 0.0873 Substituting the value of the total mass of hydrogen from step 1: Total mass of compound = 8 amu / 0.0873 ≈ 91.62 amu

Calculate the total mass of Element E in the compound

We are given that element E constitutes 91.27% of the compound. Therefore, the total mass of E in the compound can be found by using the percentage composition: Total mass of E = (Total mass of compound) * 0.9127 Substituting the value of the total mass of the compound from step 2: Total mass of E = 91.62 amu * 0.9127 ≈ 83.62 amu

Calculate the atomic mass of Element E

The formula of the compound, E3H8, indicates that there are 3 atoms of Element E in the compound. To find the atomic mass of E, we simply divide the total mass of E in the compound by the number of E atoms: Atomic mass of E = (Total mass of E) / 3 Substituting the value of the total mass of E from step 3: Atomic mass of E = 83.62 amu / 3 ≈ 27.87 amu Thus, the atomic mass of Element E is approximately 27.87 amu.

Key concepts

Binary Compounds

Binary compounds are chemical compounds made up of exactly two different elements. In the context of this exercise, we are dealing with a compound consisting of hydrogen and an unknown element, identified as \( E \). Binary compounds are often represented by a chemical formula indicating the number of atoms of each element present. For example, \( \text{E}_3\text{H}_8 \) means there are three atoms of element \( E \) and eight atoms of hydrogen.
Understanding binary compounds is crucial for determining molecular formulas and conducting mass composition calculations, as it simplifies the process when you know there are only two types of atoms to consider. This foundational concept will help when further working with more complex compounds.

Percent Composition

Percent composition is the percentage by mass of each element in a compound. It's calculated as the mass of the element divided by the total mass of the compound, multiplied by 100.
To determine percent composition, follow these steps:

• Find the mass of each element in one mole of the compound.
• Calculate the total molecular mass of the compound.
• Divide the mass of each element by the total molecular mass and multiply by 100 to get the percent composition.

In the case of our compound \( \text{E}_3\text{H}_8 \), we know its percent composition: 91.27% \( E \) and 8.73% hydrogen. This information lets us back-calculate other properties, like atomic masses and chemical formulas.

Atomic Mass Calculation

Calculating atomic mass in a binary compound involves knowing its percent composition and total mass. In this exercise, we used the formula \( \text{E}_3\text{H}_8 \) and the percent of hydrogen (8.73%) to find the total mass of the compound.
We calculated that the total mass of hydrogen is 8 amu since there are 8 hydrogen atoms each weighing about 1 amu. Given the hydrogen percentage, we derived the total mass of the compound as approximately 91.62 amu by dividing the mass of hydrogen by 0.0873 (8.73% as a decimal).
Once we knew the total mass of the compound, we calculated the mass of \( E \), considering it makes up 91.27% of the total mass. By dividing this mass by the number of \( E \) atoms (3), we determined an approximate atomic mass for \( E \) as 27.87 amu.

Mass Percentages

Mass percentages help chemists understand the proportion of each atom in a compound relative to the overall mass. They are calculated by dividing the mass of each atom by the compound's total mass, then multiplying by 100.
In our problem, we used mass percentages to connect the percent compositions of the elements \( E \) and hydrogen with their respective masses in the compound. The method allowed us to determine the total mass of the compound (91.62 amu) and subsequently use it to find elemental masses and atomic mass.
Recognizing and applying mass percentages is important for tasks such as verifying purity, comparing different compounds, or computing other chemical and physical properties.