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Given that \(555 \mathrm{~mL}\) of sulfur dioxide at STP dissolves in \(0.250 \mathrm{~L}\) 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) 1.587 g of SO2, (b) 1.492 x 10^22 molecules, (c) 0.0991 M.

Step by step solution

01

Understanding Standard Temperature and Pressure (STP)

At standard temperature and pressure (STP), which is 0°C (273.15 K) and 1 atmosphere of pressure, one mole of any gas occupies 22.4 L. This information is crucial for converting the volume of gas to moles.
02

Converting Volume of SO2 to Moles

Given the volume of sulfur dioxide is 555 mL, we first convert this to liters: \(555 \text{ mL} = 0.555 \text{ L}\). Using the molar volume at STP, we find the number of moles: \(\text{Moles of } \text{SO}_2 = \frac{0.555 \text{ L}}{22.4 \text{ L/mol}} = 0.02477 \text{ moles}\).
03

Calculating the Mass of SO2

To find the mass of \(\text{SO}_2\), use its molar mass. The molar mass of \(\text{SO}_2\) is approximately 64.07 g/mol. Calculate the mass using the number of moles: \(\text{Mass of } \text{SO}_2 = 0.02477 \text{ moles} \times 64.07 \text{ g/mol} = 1.587 \text{ g}\).
04

Determining the Number of Molecules of SO2

Use Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol) to calculate the number of molecules: \(\text{Molecules of } \text{SO}_2 = 0.02477 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.492 \times 10^{22} \text{ molecules}\).
05

Finding Molar Concentration of H2SO3 Solution

Assuming all dissolved \(\text{SO}_2\) reacts to form sulfurous acid \((\text{H}_2\text{SO}_3)\), the moles of \(\text{SO}_2\) will be equal to the moles of \(\text{H}_2\text{SO}_3\). The molar concentration is then: \(\text{Concentration of } \text{H}_2\text{SO}_3 = \frac{0.02477 \text{ moles}}{0.250 \text{ L}} = 0.0991 \text{ M}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mole Concept
The mole concept is a fundamental idea in chemistry that helps us understand the amount of substance in terms of the number of particles it contains. A mole is a unit that is used to express the quantity of a substance. Earthly materials and chemical constituents can contain a vast number of atoms or molecules, which makes direct counting impossible. To address this, chemists use moles to count particles in a manageable way.

One mole is equivalent to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles, be they atoms, molecules, ions, or electrons. This large number bridges the microcosm of individual particles and the human-scale quantities we measure in grams and liters. For molecules in gaseous states, the mole concept connects directly to their physical volumes through molar volume under STP conditions.
  • 1 mole = \(6.022 \times 10^{23}\) particles
  • Molar mass (in grams/mole) connects the number of moles to mass
  • At STP, 1 mole of gas occupies 22.4 L
Standard Temperature and Pressure (STP)
Standard conditions known as Standard Temperature and Pressure, or STP, provide a universal reference for reporting properties of gases. STP is set at 0°C (or 273.15 K) and 1 atmosphere of pressure. This standardization is crucial because gas properties, like volume, are highly sensitive to temperature and pressure.

Under these conditions, gases exhibit predictable behaviors that facilitate calculations in stoichiometry. A key feature of STP is knowing that one mole of any ideal gas occupies 22.4 liters. This understanding streamlines computations by allowing volume-to-mole conversions without first recalibrating for differing pressures or temperatures each time.
  • 0°C or 273.15 K is the temperature at STP
  • 1 atmosphere is the pressure at STP
  • 1 mole of gas = 22.4 L at STP
Molar Concentration
Molar concentration, often known as molarity, impacts how solutions are characterized and used in chemical reactions. It measures how much moles of solute are present in a given volume of solution, typically expressed in moles per liter (M). The formula used to find molarity is:

\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\]

Molarity is crucial for calculations in chemistry. It enables predictions on the outcomes of chemical reactions and solutions needed for stoichiometry problems. Calculating the molarity of a solution, like the sulfurous acid in our example, involves recognizing how much \(\text{SO}_2\) dissolves and reacts within a known solution volume.
  • Expressed in moles/liter (M)
  • Essential for accurately preparing chemical reactions
  • Key in determining solution compositions and hardness

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Most popular questions from this chapter

Given that \(1.00 \mathrm{~L}\) of carbon dioxide at STP dissolves in \(500.0 \mathrm{~mL}\) of solution, draw a mole concept map and calculate each of the following: (a) grams of \(\mathrm{CO}_{2}\) gas (at STP) dissolved in the solution (b) molecules of \(\mathrm{CO}_{2}\) gas dissolved in the solution (c) molar concentration of the carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{3}\) solution

State the physical quantity corresponding to each of the following metric units. (a) \(\mathrm{m} / \mathrm{s}\) (b) \(\mathrm{g} / \mathrm{mL}\) (c) \(\mathrm{cal} /\left(\mathrm{g} \times{ }^{\circ} \mathrm{C}\right)\) (d) \(\mathrm{g}\) solute \(/ 100-\mathrm{g}\) solution

Steering rockets on the space shuttle are powered by the reaction of hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}\), and dinitrogen tetraoxide, \(\mathrm{N}_{2} \mathrm{O}_{4}\). The reactions for making hydrazine and the reaction with dinitrogen tetraoxide are as follows: $$ \begin{array}{c} 2 \mathrm{NH}_{3}(a q)+\mathrm{NaOCl}(a q) \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}(a q)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \\ 2 \mathrm{~N}_{2} \mathrm{H}_{4}(l)+\mathrm{N}_{2} \mathrm{O}_{4}(l) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \end{array} $$ Starting with \(50.0 \mathrm{~mL}\) of \(6.00 \mathrm{M}\) ammonia and excess other reactants, calculate: (a) the mass of nitrogen gas produced (b) the volume of nitrogen gas produced at STP (c) the mass of water produced

State the physical quantity corresponding to each of the following units. (a) \(\mathrm{mm}\) (b) \(\mathrm{kg}\) (c) \(\mathrm{cm}^{3}\) (d) s (e) \({ }^{\circ} \mathrm{C}\) (f) \(\mathrm{kcal}\)

Ammonia gas, \(\mathrm{NH}_{3}\), reacts with oxygen and platinum catalyst to give \(25.0 \mathrm{~L}\) of nitrogen monoxide gas at STP according to the chemical reaction: $$ \mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \stackrel{\mathrm{Pt} / 825^{\circ} \mathrm{C}}{\longrightarrow} \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$ Draw a stoichiometry concept map and calculate: (a) the volume of ammonia that reacted at STP (b) the mass of water that was produced

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