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Magazine Chapter 16: Problem 20
Given that \(555 \mathrm{~mL}\) of sulfur dioxide at STP dissolves in 0.250 L of solution, draw a mole concept map and calculate each of the following: (a) grams of \(\mathrm{SO}_{2}\) gas (at STP) dissolved in the solution (b) molecules of \(\mathrm{SO}_{2}\) gas dissolved in the solution (c) molar concentration of the sulfurous acid, \(\mathrm{H}_{2} \mathrm{SO}_{3}\) solution
Short Answer
Expert verified
(a) ~1.59 g of SO2, (b) ~1.49 x 10^22 molecules, (c) ~0.099 M H2SO3.
Step by step solution
01
Understanding STP Conditions
Standard Temperature and Pressure (STP) refers to a temperature of 0掳C (273.15 K) and a pressure of 1 atm. At STP, one mole of any ideal gas occupies 22.4 liters.
02
Calculate Moles of SO2
Convert 555 mL to liters: 555 mL = 0.555 L. Use the molar volume at STP to find moles of SO2: \[ \text{moles of } \mathrm{SO}_2 = \frac{0.555 \text{ L}}{22.4 \text{ L/mol}} \approx 0.0248 \text{ moles} \]
03
Convert Moles to Grams
The molar mass of sulfur dioxide (SO2) is approximately 64.07 g/mol. Calculate the mass:\[ \text{mass of } \mathrm{SO}_2 = 0.0248 \text{ moles} \times 64.07 \text{ g/mol} \approx 1.59 \text{ g} \]
04
Calculate Number of Molecules
Use Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol, to find the number of molecules:\[ \text{Number of molecules} = 0.0248 \text{ moles} \times 6.022 \times 10^{23} \approx 1.49 \times 10^{22} \text{ molecules} \]
05
Calculate Molarity of H2SO3
Assuming all dissolved SO2 becomes H2SO3 in the solution, we use the moles of SO2 to find the molarity:\[ \text{Molarity} = \frac{0.0248 \text{ moles}}{0.250 \text{ L}} \approx 0.0992 \text{ M} \]
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
STP (Standard Temperature and Pressure)
Standard Temperature and Pressure, or STP, is a set of conditions often used in chemistry to simplify calculations regarding gases. Under STP conditions, the temperature is defined as 0掳C or 273.15 K, and the pressure is set to 1 atmosphere (atm). These conditions are convenient because, at STP, one mole of an ideal gas occupies a volume of 22.4 liters. This fixed volume per mole makes it much easier to compare different gases and predict how they will behave under these standard conditions.
Moles
The concept of a mole is fundamental in chemistry for quantifying the amount of substance. One mole corresponds to Avogadro's number, which is approximately 6.022 x 10^23 entities, be they atoms, molecules, or other particles. This quantity was chosen because it links the mass of an element or compound in grams to the number of atoms or molecules atomically. Thus, when we talk about moles, we are relating the microscopic world of individual molecules to the macroscopic world we can observe and measure.
Mole to Gram Conversion
Converting moles to grams is a common task in chemistry and requires knowledge of the substance's molar mass, which is the mass of one mole of a given substance. This value is typically found on the periodic table, expressed in grams per mole (g/mol). For instance, sulfur dioxide (SO2) has a molar mass of approximately 64.07 g/mol. Therefore, to find the number of grams in a sample, you multiply the number of moles by the molar mass:
- mass in grams = moles x molar mass (g/mol)
Avogadro's Number
Avogadro's number is a fundamental constant in chemistry, named after the scientist Amedeo Avogadro. It is defined as the number of atoms, molecules, or particles in one mole, which is approximately 6.022 x 10^23. This large number bridges the gap between the atomic scale and the scale we use in laboratories. Avogadro's number allows chemists to perform calculations to determine the number of particles in a sample, given the amount in moles, using:
- number of particles = moles x Avogadro's number
Molar Concentration
Molar concentration, or molarity, measures the concentration of a solute in a solution. It's expressed as the number of moles of solute per liter of solution, represented with the unit M (moles/L). Molarity is a vital concept in preparing solutions and performing stoichiometric calculations. If we dissolve sulfur dioxide in water to form sulfurous acid, we use the known moles of gas to calculate the molarity of the resultant solution:
- Molarity (M) = moles of solute / volume of solution in liters
Sulfur Dioxide (SO2)
Sulfur dioxide is a colorless gas with a pungent odor and is an important chemical in industrial processes. It is produced naturally and anthropogenically through combustion processes, especially burning sulfur-rich fossil fuels. In the context of chemistry, sulfur dioxide is often involved in reactions forming acids, like sulfurous acid (H2SO3). At STP, using the molar volume, we can determine how much SO2 is present in a given volume of gas. This information is crucial when calculating its transformation or use in solutions.
Sulfurous Acid (H2SO3)
Sulfurous acid, H2SO3, is a compound formed when sulfur dioxide is dissolved in water. Although its existence in solution is often transient, it's an essential intermediate in many chemical processes. In this exercise's context, the gas sulfur dioxide dissolves in water, forming sulfurous acid. Understanding this transformation is key to solving problems involving the concentration of reactants and products in a solution. The molarity of sulfurous acid can be calculated using the moles of dissolved SO2, showcasing how gases interact with solvents and change states in chemical reactions.
