Question

In which of the following compounds, the weight percentage of \(\mathrm{C}\) and \(\mathrm{H}\) are 80 and 20 respectively? (a) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (b) \(\mathrm{CH}_{4}\) (c) \(\mathrm{C}_{6} \mathrm{H}_{6}\) (d) \(\mathrm{C}_{2} \mathrm{H}_{3}\)

Short answer

The compound is \(\mathrm{C}_{2} \mathrm{H}_{6}\).

Step-by-step solution

Understand the Required Weight Percentage

We need to find the compound in which carbon (C) makes up 80% of the total weight and hydrogen (H) makes up 20%. Weight percentage can be calculated by dividing the total weight of the specific element by the total molecular weight of the compound, then multiplied by 100.

Calculate the Molecular Weight of Each Compound

For each compound, calculate the molecular weight using atomic weights: \(C = 12 \text{ u}\) and \(H = 1 \text{ u}\). - \(\mathrm{C}_{2} \mathrm{H}_{6}\): \(2 \times 12 + 6 \times 1 = 24 + 6 = 30 \text{ u}\)- \(\mathrm{CH}_{4}\): \(1 \times 12 + 4 \times 1 = 12 + 4 = 16 \text{ u}\)- \(\mathrm{C}_{6} \mathrm{H}_{6}\): \(6 \times 12 + 6 \times 1 = 72 + 6 = 78 \text{ u}\)- \(\mathrm{C}_{2} \mathrm{H}_{3}\): \(2 \times 12 + 3 \times 1 = 24 + 3 = 27 \text{ u}\)

Calculate the Weight Percentage of C and H for Each Compound

For each compound, calculate and compare:- \(\mathrm{C}_{2} \mathrm{H}_{6}\): - % C: \(\frac{24}{30} \times 100 = 80\%\) - % H: \(\frac{6}{30} \times 100 = 20\%\)- \(\mathrm{CH}_{4}\): - % C: \(\frac{12}{16} \times 100 = 75\%\) - % H: \(\frac{4}{16} \times 100 = 25\%\)- \(\mathrm{C}_{6} \mathrm{H}_{6}\): - % C: \(\frac{72}{78} \times 100 \approx 92.3\%\) - % H: \(\frac{6}{78} \times 100 \approx 7.7\%\)- \(\mathrm{C}_{2} \mathrm{H}_{3}\): - % C: \(\frac{24}{27} \times 100 \approx 88.9\%\) - % H: \(\frac{3}{27} \times 100 \approx 11.1\%\)

Identify the Correct Compound

From the calculations, only \(\mathrm{C}_{2} \mathrm{H}_{6}\) has a weight percentage of 80% carbon and 20% hydrogen. Therefore, \(\mathrm{C}_{2} \mathrm{H}_{6}\) is the correct compound.

Key concepts

Molecular Weight

Molecular weight is an important concept in chemistry that helps us understand the mass of a chemical compound. It is calculated by adding up the atomic weights of all the atoms present in a molecule. The atomic weight of an element is usually measured in atomic mass units (u), where one atomic mass unit is defined as 1/12 of the mass of a carbon-12 atom.
For example, to find the molecular weight of a compound like \(\mathrm{C}_{2} \mathrm{H}_{6}\) (ethane), we look at the atomic weights: carbon (C) has an atomic weight of 12 u, and hydrogen (H) weighs 1 u per atom. To calculate the molecular weight, we sum up the contribution of each atom:

• Carbon: \(2 \times 12 \text{ u} = 24 \text{ u}\)
• Hydrogen: \(6 \times 1 \text{ u} = 6 \text{ u}\)

Hence, the molecular weight of \(\mathrm{C}_{2} \mathrm{H}_{6}\) is \(30 \text{ u}\). Understanding molecular weight helps in determining other properties like the percent composition of elements in a compound.

Atomic Weights

Atomic weight, often referred to as relative atomic mass, is a fundamental concept in chemistry. It refers to the average mass of atoms of an element, calculated using the relative natural abundance of each isotope of that element. This measurement is crucial as it aids in calculating the molecular weights of compounds.
For example, the atomic weight of hydrogen (H) is approximately 1 u and that of carbon (C) is approximately 12 u. These values allow chemists to predict how elements will combine to form compounds.
To get a sense of scale, if we consider any chemical reaction, knowing the atomic weights of the involved elements enables precise calculation of reactant and product masses, ensuring the reaction proceeds correctly and efficiently. Atomic weights are foundational in not only theoretical calculations but also practical applications in laboratories around the world.

Chemical Compounds

Chemical compounds are substances consisting of two or more different elements that are chemically bonded together. Understanding compounds is essential for exploring the properties of substances and their reactions. Compounds are characterized by specific chemical formulas that indicate the types and numbers of atoms involved.
For instance, \(\mathrm{C}_{2} \mathrm{H}_{6}\) (ethane) is a compound made of carbon and hydrogen. The chemical formula shows it consists of two carbon atoms bonded with six hydrogen atoms.
The study of chemical compounds covers various aspects like bonding types (ionic, covalent, metallic), reactivity, and physical properties such as boiling points or solubility. This knowledge is crucial for fields like pharmaceuticals, agriculture, and environmental science. Chemistry allows us to break down compounds back into elements or rearranging them into new compounds through various chemical reactions.

Percent Composition

Percent composition is the percentage by mass of each element in a compound. Knowing a compound's percent composition is valuable for understanding its chemical makeup and purity. It's calculated by taking the mass of an individual element divided by the total molecular weight of the compound, and then multiplying by 100.
For example, in the compound \(\mathrm{C}_{2} \mathrm{H}_{6}\), we want to determine the percent composition of carbon and hydrogen:

• For Carbon: \(\left(\frac{24}{30}\right) \times 100 = 80\%\)
• For Hydrogen: \(\left(\frac{6}{30}\right) \times 100 = 20\%\)

This calculation reveals that 80% of the compound’s mass is carbon, and 20% is hydrogen.
Percent composition is useful in fields such as materials science and nutrition, where the makeup of a substance needs to be precisely understood. It's also pivotal in determining empirical and molecular formulas of unknown compounds.