Question

Select the correct alternative from the given choices. \(20 \mathrm{cc}\) of a hydrocarbon on complete combustion gave \(80 \mathrm{cc}\) of \(\mathrm{CO}_{2}\) and \(100 \mathrm{cc}\) of \(\mathrm{H}_{2} \mathrm{O}\) at \(\mathrm{STP}\). The empirical formula of that compound is (a) \(\mathrm{C}_{2} \mathrm{H}_{5}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (c) \(\mathrm{C}_{3} \mathrm{H}_{8}\) (d) \(\mathrm{C}_{4} \mathrm{H}_{10}\)

Short answer

a) CH b) C2H4 c) C3H8 d) CH4 Answer: c) C3H8

Step-by-step solution

Calculate the moles of CO₂ and H₂O produced

To do this, we will use the molar volume of an ideal gas at standard temperature and pressure (STP), which is 22.4 liters (L) or 22,400 cc per mole. Therefore, we can calculate the moles of CO₂ and H₂O as: Moles of CO₂ = \(\frac{80 \,\text{cc}}{22,400 \,\text{cc/mol}}\) Moles of H₂O = \(\frac{100 \,\text{cc}}{22,400 \,\text{cc/mol}}\)

Determine the moles of carbon and hydrogen in the initial hydrocarbon

Since CO₂ is produced by the combustion of carbon, the moles of CO₂ can be used to calculate moles of carbon in the hydrocarbon: Moles of C = Moles of CO₂ For hydrogen, we know that a H₂O molecule has two hydrogen atoms. Therefore, moles of hydrogen can be calculated as: Moles of H = 2 × Moles of H₂O

Calculate the C-to-H mole ratio

Now that we have the moles of C and H in the initial hydrocarbon, we can find the simplest whole number ratio between them by dividing each by their respective moles: C-to-H ratio = \(\frac{\text{Moles of C}}{\text{Moles of H}}\)

Determine the empirical formula

Based on the C-to-H ratio, we can now choose the correct empirical formula from the given options. After performing the calculations: Moles of CO₂ = \(\frac{80}{22,400}\) = 0.00357 moles Moles of H₂O = \(\frac{100}{22,400}\) = 0.00446 moles Moles of C = 0.00357 moles Moles of H = 2 × 0.00446 = 0.00893 moles C-to-H ratio = \(\frac{0.00357}{0.00893}\) = 0.40 (approximately) The closest whole number ratio of C-to-H is 1:3 (C3H8). Therefore, the correct answer is (c) \(\text{C}_3\text{H}_8\).

Key concepts

Molar Volume at STP

The concept of molar volume at STP (Standard Temperature and Pressure) is fundamental in chemistry for calculations involving gases. At STP, 1 mole of any ideal gas occupies the same volume. This is defined as 22.4 liters or 22,400 cubic centimeters (cc).

STP conditions are defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (101.3 kPa). The uniformity of molar volume across different gases at STP simplifies gas-related calculations, particularly those involving reactions and stoichiometry.

For example, in the provided problem, the given volumes of \( ext{CO}_2\) and \( ext{H}_2 ext{O}\) are used alongside the molar volume to calculate the number of moles produced from the hydrocarbon combustion. This enables the determination of elemental composition within the compound.

Combustion Analysis

Combustion analysis is a technique used to determine the composition of an unknown hydrocarbon compound. This involves burning, or combusting, a sample of the compound in excess oxygen to produce carbon dioxide (CO₂) and water (H₂O). By measuring the quantities of these two products, we can infer the amount of carbon and hydrogen initially present in the compound.

In the exercise, the combustion of the hydrocarbon produces a certain volume of CO₂ and H₂O, which can be converted to moles using molar volume, allowing us to further analyze the compound's composition. This method aids in determining the empirical formula, which is the simplest whole-number ratio of elements in the compound.

Understanding the basics of combustion analysis is crucial for learners to grasp how chemists deduce the composition of organic compounds through experiments.

Hydrocarbon Combustion

Hydrocarbon combustion is the burning of a hydrocarbon in the presence of oxygen to produce carbon dioxide, water, and energy. This reaction is exothermic, meaning it releases heat.

The general equation for burning a hydrocarbon \( ext{C}_x ext{H}_y\) can be written as: \text{C}_x ext{H}_y + ext{O}_2 ightarrow ext{CO}_2 + ext{H}_2 ext{O}\. Through careful measurement, combustion analysis enables the determination of the hydrocarbon's composition from these products.

In the given problem, the combustion results in specific amounts of CO₂ and H₂O, which help derive the empirical formula. Understanding the reaction mechanism is essential for solving problems related to hydrocarbon analysis and deducing elemental ratios.

Mole Concept

The mole concept is a fundamental unit in chemistry that allows chemists to count particles like atoms, molecules, or ions by weighing them. One mole is defined as Avogadro's number, approximately \(6.022 \times 10^{23}\) particles of that substance.

In gas reactions, the mole concept connects directly with the molar volume at STP. For instance, in the context of the exercise, measuring the moles of \( ext{CO}_2\) and \( ext{H}_2 ext{O}\) informs us about the carbon and hydrogen content present in the original hydrocarbon.

Using molar calculations allows for the determination of empirical formulas and supports the stoichiometric understanding required to solve complex chemical reactions, making it an indispensable tool in quantitative chemistry.