Question

\(0.765 \mathrm{~g}\) of an acid gives \(0.535 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.14 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\). Then the ratio of the percentage of carbon and hydrogen is: (a) \(1: 9\) (b) \(20: 16\) (c) \(18: 11\) (d) \(19: 2\)

Short answer

The correct answer is (d) 19:2.

Step-by-step solution

Calculate Moles of Carbon in CO2

Given that the molar mass of CO₂ is 44 g/mol (12 g/mol is carbon, 32 g/mol is oxygen). From 0.535 g of CO₂, we can calculate the moles of carbon:\[ \text{Moles of } \text{CO}_2 = \frac{0.535 \text{ g}}{44 \text{ g/mol}} = 0.01216 \text{ mol} \]As each mole of CO₂ has one mole of carbon, the moles of carbon are also 0.01216 mol.

Calculate Mass of Carbon

The mass of carbon is calculated using its atomic mass (12 g/mol):\[ \text{Mass of Carbon} = 0.01216 \text{ mol} \times 12 \text{ g/mol} = 0.14592 \text{ g} \]

Calculate Percentage of Carbon in Acid

To find the percentage of carbon in the acid, use the formula:\[ \text{Percentage of Carbon} = \left( \frac{0.14592 \text{ g}}{0.765 \text{ g}} \right) \times 100 = 19.07\% \]

Calculate Moles of Hydrogen in H2O

The molar mass of H₂O is 18 g/mol (2 g/mol is hydrogen, 16 g/mol is oxygen). From 0.14 g of H₂O, calculate the moles of hydrogen:\[ \text{Moles of } \text{H}_2\text{O} = \frac{0.14 \text{ g}}{18 \text{ g/mol}} = 0.00778 \text{ mol} \]Since each mole of H₂O has two moles of hydrogen, the moles of hydrogen are:\[ 0.00778 \text{ mol} \times 2 = 0.01556 \text{ mol} \]

Calculate Mass of Hydrogen

The mass of hydrogen is calculated using its atomic mass (1 g/mol):\[ \text{Mass of Hydrogen} = 0.01556 \text{ mol} \times 1 \text{ g/mol} = 0.01556 \text{ g} \]

Calculate Percentage of Hydrogen in Acid

To find the percentage of hydrogen in the acid, use the formula:\[ \text{Percentage of Hydrogen} = \left( \frac{0.01556 \text{ g}}{0.765 \text{ g}} \right) \times 100 = 2.03\% \]

Calculate Ratio of Percentage of Carbon to Hydrogen

Using the percentages calculated previously:\[ \text{Ratio} = \frac{19.07\%}{2.03\%} \approx 9.39:1 \]Round to nearest whole number:\[ 19:2 \]

Compare with Given Options

The calculated ratio 19:2 matches option (d). Therefore, the correct answer is (d) 19:2.

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that helps us relate different macroscopic properties to the atomic scale. A mole is a unit that represents a specific number of particles, usually atoms or molecules. One mole is equal to Avogadro's number, which is approximately \( 6.022 \times 10^{23} \) particles.
In the context of our exercise, the mole concept allows us to convert the mass of a compound like \( \text{CO}_2 \) or \( \text{H}_2\text{O} \) into the number of moles. This is done by dividing the given mass by the molar mass of the compound. For instance:

• Mole of \( \text{CO}_2 \): \( \frac{0.535 \text{ g}}{44 \text{ g/mol}} = 0.01216 \text{ mol} \)
• Mole of \( \text{H}_2\text{O} \): \( \frac{0.14 \text{ g}}{18 \text{ g/mol}} = 0.00778 \text{ mol} \)

The concept is particularly useful as it helps in determining the amount of individual atoms, such as carbon and hydrogen in the compounds, by using their molar mass (e.g., \( 12 \text{ g/mol} \) for carbon and \( 1 \text{ g/mol} \) for hydrogen). Understanding moles is crucial in solving the percentage composition of compounds, as it allows us to calculate the proportion of each element within a compound's total mass.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of bonds. In the exercise, the acid breaks down into \( \text{CO}_2 \) and \( \text{H}_2\text{O} \). During such decomposition reactions, it’s important to track which elements are present and how they rearrange.
In our example:

• The carbon from the acid ends up in \( \text{CO}_2 \).
• The hydrogen originally found in the acid contributes to forming \( \text{H}_2\text{O} \).

Understanding these transformations is critical. Consider the calculation of moles from a breakdown product like \( \text{CO}_2 \) as a means to determine the original amount of carbon in the acid. Similarly, using the molecular composition of \( \text{H}_2\text{O} \) gives insight into the hydrogen present initially. Chemical reactions emphasize the conservation of mass, meaning all atoms present in the reactants must be accounted for in the products, facilitating calculations of composition and yield.

Percentage Composition

The percentage composition of a compound refers to the percentage by mass of each element in the compound. It is essential for understanding the makeup of chemical substances. The formula for percentage composition is:\[ \text{Percentage of Element} = \left( \frac{\text{Mass of Element}}{\text{Total Mass of Compound}} \right) \times 100 \]In the given exercise, we looked at the percentage of carbon and hydrogen in the acid:

• Carbon: \( \left( \frac{0.14592\, \text{g}}{0.765\, \text{g}} \right) \times 100 = 19.07\% \)
• Hydrogen: \( \left( \frac{0.01556\, \text{g}}{0.765\, \text{g}} \right) \times 100 = 2.03\% \)

Calculating the percentage composition helps in determining the purity and empirical formulas of compounds. It’s a critical step to compare the elemental proportion and eventually to find the ratio between these percentages, simplifying to the smallest whole number ratio for ease of interpretation.
In this case, calculating the ratio of carbon to hydrogen using their percentages gave us \( 19:2 \), corresponding to one of the given options. This demonstrates how percentage composition ties into problem-solving in stoichiometry.