Question

\(\infty 0\) Section \(2.9\) introduced the idea of structural isomerism, with 1-propanol and 2-propanol as examples. Determine which of these properties would distinguish these two substances: (a) boiling point, (b) combustion analysis results, (c) molecular weight, (d) density at a given temperature and pressure. You can check on the properties of these two compounds in Wolfram Alpha (http://www.wolframalpha.com/) or the CRC Handbook of Chemistry and Physics. \(3.110\) A particular coal contains \(2.5 \%\) sulfur by mass. When this coal is burned at a power plant, the sulfur is converted into sulfur dioxide gas, which is a pollutant. To reduce sulfur dioxide emissions, calcium oxide (lime) is used. The sulfur dioxide reacts with calcium oxide to form solid calcium sulfite. (a) Write the balanced chemical equation for the reaction. (b) If the coal is burned in a power plant that uses 2000 tons of coal per day, what mass of calcium oxide is required daily to eliminate the sulfur dioxide? (c) How many grams of calcium sulfite are produced daily by this power plant?

Short answer

(a) Boiling points or other physical properties like density at given temperature and pressure can distinguish 1-propanol and 2-propanol. However, molecular weight and combustion analysis results would be identical for both compounds. (b) The power plant needs 87.45 tons of calcium oxide daily to eliminate the sulfur dioxide emissions. (c) The power plant produces 187.25 tons of calcium sulfite daily.

Step-by-step solution

Analyze the properties of 1-propanol and 2-propanol

By searching the properties of 1-propanol and 2-propanol on Wolfram Alpha or in the CRC Handbook of Chemistry and Physics, we can compare their boiling points, combustion analysis results, molecular weights, and densities at a given temperature and pressure. This information will help us determine which properties are unique to each substance.

Write the balanced chemical equation

For the reaction between sulfur dioxide (SO_2) and calcium oxide (CaO), the balanced chemical equation is: SO_2 + CaO -> CaSO_3 This shows that one mole of sulfur dioxide reacts with one mole of calcium oxide to produce one mole of calcium sulfite (CaSO_3).

Calculate the mass of calcium oxide needed daily

First, we'll find the mass of sulfur in 2000 tons of coal: 2000 tons * 0.025 = 50 tons of sulfur Next, we'll convert the mass of sulfur to moles. The molar mass of sulfur (S) is 32.06 g/mol: 50 tons * 1000 kg/ton * 1000 g/kg / 32.06 g/mol = 1559056.17 moles of sulfur Since each mole of sulfur produces one mole of sulfur dioxide (SO_2) when burned, the number of moles of SO_2 is the same as the number of moles of sulfur. Hence, 1559056.17 moles of SO_2 are produced daily by the power plant. According to the balanced chemical equation, one mole of SO_2 reacts with one mole of CaO. Therefore, the mass of calcium oxide required on daily basis is equal to the number of moles of SO_2 multiplied by the molar mass of calcium oxide. The molar mass of calcium oxide (CaO) is 56.08 g/mol: 1559056.17 moles of SO_2 * 56.08 g/mol of CaO = 87445192.91 g/day 87445192.91 g/day * 1 ton/1000000 g = 87.45 tons/day of CaO So, the power plant needs 87.45 tons of calcium oxide daily to eliminate the sulfur dioxide emissions.

Calculate the mass of calcium sulfite produced daily

According to the balanced chemical equation, each mole of SO_2 reacts with one mole of CaO to produce one mole of calcium sulfite (CaSO_3). Therefore, the number of moles of CaSO_3 produced daily is equal to the number of moles of SO_2. The molar mass of calcium sulfite (CaSO_3) is 120.14 g/mol. So, the mass of calcium sulfite produced daily by the power plant is: 1559056.17 moles of CaSO_3 * 120.14 g/mol of CaSO_3 = 187245030.42 g/day 187245030.42 g/day * 1 ton/1000000 g = 187.25 tons/day of CaSO_3 The power plant produces 187.25 tons of calcium sulfite daily. Recap of results: (a) Boiling points or other physical properties like density at given temperature and pressure can distinguish 1-propanol and 2-propanol. However, molecular weight and combustion analysis results would be identical for both compounds. (b) The power plant needs 87.45 tons of calcium oxide daily to eliminate the sulfur dioxide emissions. (c) The power plant produces 187.25 tons of calcium sulfite daily.

Key concepts

Boiling Point Differentiation

When discussing structural isomers, such as 1-propanol and 2-propanol, boiling point differentiation often serves as a reliable property for distinguishing between the two. Structural isomers have the same molecular formula but differ in the arrangement of atoms within the molecule. This rearrangement can lead to variations in physical properties, including boiling points.

Boiling point is the temperature at which a liquid's vapor pressure equals the external pressure surrounding the liquid. Consequently, a molecule's intermolecular forces greatly influence its boiling point. Isomers with stronger intermolecular forces —for instance, those with more hydrogen-bonding capabilities— will generally have a higher boiling point.

In the case of 1-propanol and 2-propanol, the position of the hydroxyl group (-OH) greatly affects hydrogen bonding. 1-propanol has its hydroxyl group at the end of the chain, allowing it to engage in hydrogen bonding more effectively than 2-propanol, which has the hydroxyl group in the middle. As a result, 1-propanol typically exhibits a higher boiling point than 2-propanol.

Combustion Analysis

Combustion analysis is a laboratory method used to determine the elemental composition of a compound, particularly organic compounds. In this technique, a known mass of a substance is burned in excess oxygen, and the resultant products—carbon dioxide and water—are measured.

For structurally isomeric compounds such as 1-propanol and 2-propanol, the combustion analysis would yield the same ratios of carbon dioxide and water since they contain the same number of hydrogen, carbon, and oxygen atoms. Consequently, this analysis would not effectively differentiate between the two. However, it is crucial in confirming the empirical formula of an unknown organic compound and serves as an essential step in detailed chemical analysis.

Chemical Reaction Balancing

Balancing chemical reactions is a fundamental aspect of stoichiometry and ensures that matter is conserved in accordance with the Law of Conservation of Mass. During balancing, each element's number of atoms is made equal on both the reactant and product sides of the equation. This is essential as it governs the ratios in which substances react and the quantities in which they are formed.

For example, the reaction between sulfur dioxide and calcium oxide to form calcium sulfite can be balanced as follows: \[\text{SO}_2 + \text{CaO} \rightarrow \text{CaSO}_3\].

Here, there is one sulfur atom, three oxygen atoms, and one calcium atom on both sides, demonstrating a balanced reaction. Correctly balancing chemical reactions is fundamental in predicting the yields of products and the amounts of reactants needed, as shown in step 2 of the provided solution.

Stoichiometric Calculations

Stoichiometry involves the calculation of the quantities of reactants and products involved in chemical reactions. It is a foundational concept in chemistry that relies on the balanced chemical equation and serves as the bridge between the molecular scale and the real-world mass scale calculations.

In the given exercise, stoichiometric calculations help us to determine the necessary mass of calcium oxide needed to react with the sulfur in coal and produce calcium sulfite. You begin by calculating the moles of sulfur, and then, based on the balanced equation, deduce the corresponding moles and thus the mass of calcium oxide and calcium sulfite required or produced.

This process is critical for anything from industrial chemical manufacturing to environmental management, exemplified by a power plant's need for lime to reduce pollutant emissions. The precise application of stoichiometric principles ensures the efficient and environmentally responsible use of chemicals, as seen in steps 3 and 4 of the solution.