Question

In a hydrocarbon, mass ratio of hydrogen and carbon is \(1: 3\), the empirical formula of hydrocarbon is: (a) \(\mathrm{CH}_{2}\) (b) \(\mathrm{CH}_{4}\) (c) \(\mathrm{CH}_{3}^{-}\) (d) \(\mathrm{CH}\)

Short answer

The empirical formula is \( \mathrm{CH}_{4} \).

Step-by-step solution

Understand the Mass Ratio

We are given that the mass ratio of hydrogen to carbon in the hydrocarbon is 1:3. This means for every 1 part of hydrogen by mass, there are 3 parts of carbon.

Determine Atomic Masses

The atomic mass of hydrogen is approximately 1 g/mol, and the atomic mass of carbon is approximately 12 g/mol.

Convert Mass Ratio to Mole Ratio

To find the empirical formula, convert the given mass ratio to a molar ratio. The amount of hydrogen to carbon in moles can be calculated as follows: For hydrogen, divide the mass by its atomic mass (1 g/mol); for carbon, divide the mass by its atomic mass (12 g/mol). This results in:Hydrogen: \( \frac{1}{1} = 1 \)Carbon: \( \frac{3}{12} = 0.25 \).

Simplify the Mole Ratio

Now, divide both results from Step 3 by the smallest number of moles to simplify the ratio:Hydrogen: \( \frac{1}{0.25} = 4 \)Carbon: \( \frac{0.25}{0.25} = 1 \).

Write the Empirical Formula

The simplified mole ratio reveals the ratio of hydrogen to carbon is 4:1. Therefore, the empirical formula is \( \mathrm{CH}_{4} \).

Key concepts

Chemical Formulas

Chemical formulas are a fundamental concept in chemistry, revealing the composition of molecules and compounds. They tell us how many atoms of each element are present in a compound.
One common type of chemical formula is the empirical formula, which provides the simplest whole-number ratio of the elements in a compound.
For example, if a compound contains carbon and hydrogen atoms, the empirical formula helps us understand their basic ratio, like in a hydrocarbon where hydrogen and carbon are involved.

• They do not provide information about the actual number of atoms but rather the ratio.
• Understanding chemical formulas is crucial to deciphering the properties and behaviors of compounds.

Our exercise application towards hydrocarbons emphasizes these concepts by focusing on determining the simplest representation of atoms involved.

Hydrocarbons

Hydrocarbons are organic compounds made exclusively of hydrogen and carbon atoms.
They are the primary constituents of many fuels and are categorized into different types such as alkanes, alkenes, and alkynes, depending on the nature of chemical bonds between carbon atoms.
In the context of empirical formulas, hydrocarbons are a common area of study because their simple structure allows for easy understanding of mole concepts.

• Alkanes, for instance, have the general formula of C\(n\)H\(2n+2\), where n is the number of carbon atoms.
• By understanding the mass ratios of hydrogen and carbon, we can determine the empirical formula for any hydrocarbon.

This practice deepens comprehension of molecular composition and is vital for further studies in organic chemistry.

Mole Ratio

The mole ratio is a crucial concept in determining empirical formulas, as it gives the proportion of moles of each element in a compound.
It is derived from converting mass ratios into a form that expresses how many moles of each element are present relative to each other.
This conversion is vital since it translates elemental masses into a common measuring unit.

• In the given example, a mass ratio is converted by dividing each element’s mass by its atomic mass.
• The resulting values are then simplified to achieve a whole-number ratio, essential for formulating the empirical formula.

Understanding and applying mole ratios enables us to predict and equalize chemical reactions more effectively, as it builds on the idea of balancing the number of atoms.

Atomic Mass

Atomic mass is the mass of a single atom of a chemical element, measured in atomic mass units (amu).
It's an average of all the isotopes of an element, weighted by their abundance.
Knowing the atomic masses of elements is critical when converting mass ratios to mole ratios in chemistry.

• For instance, hydrogen has an atomic mass of approximately 1 g/mol, while carbon’s atomic mass is about 12 g/mol.
• Using these values, we can transition from mass to moles, which is an integral step in finding empirical formulas.

This concept is foundational to understanding how different atoms contribute to the chemical composition and structure of substances.

Stoichiometry

Stoichiometry involves measuring and calculating the relationships between reactants and products in chemical reactions.
It is a core principle that relies heavily on the mole concept and the conservation of mass.
In essence, stoichiometry ensures that a chemical equation is balanced, meaning the number of atoms for each element is equal on both the reactant and product sides.

• Through stoichiometry, we can determine how much of a substance will react or be produced.
• The process requires a solid grasp of mole ratios, atomic masses, and empirical formulas.

This knowledge is essential not only for predicting the outcomes of chemical reactions but also for synthesizing new compounds.