/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 143 The reaction \(8 \mathrm{H}_{2}(... [FREE SOLUTION] | 91Ó°ÊÓ

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The reaction \(8 \mathrm{H}_{2}(g)+\mathrm{S}_{8}(l) \longrightarrow 8 \mathrm{H}_{2} \mathrm{~S}(g)\) is run at \(125^{\circ} \mathrm{C}\) and a constant pressure of \(12.0\) atm. Assuming complete reaction, what mass of \(\mathrm{S}_{8}\) would be required to produce \(6.00 \mathrm{X}\) \(10^{2} \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{~S}\) gas under these conditions?

Short Answer

Expert verified
Approximately 7.03 grams of \(\mathrm{S}_{8}\) is needed.

Step by step solution

01

Convert Volume to Liters

Convert the volume of hydrogen sulfide gas from milliliters to liters. Since 1 L = 1000 mL, \[6.00 \times 10^{2} \text{ mL} = 0.600 \text{ L}\]
02

Calculate Moles of Gas Using Ideal Gas Law

Apply the ideal gas law \(PV = nRT\) to find the number of moles of \(\mathrm{H}_{2} \mathrm{~S}\). Use \(R = 0.0821 \text{ L atm/mol K}\), \(P = 12.0 \text{ atm}\), \(V = 0.600 \text{ L}\), and convert temperature to Kelvin: \[T = 125^{\circ} \text{C} = 398.15 \text{ K}\]Solving for \(n\):\[12.0 \times 0.600 = n \times 0.0821 \times 398.15\]Calculate \(n\):\[n \approx \frac{12.0 \times 0.600}{0.0821 \times 398.15} \approx 0.219 \text{ moles}\]
03

Determine Moles of S8 Required

From the balanced chemical equation, the stoichiometry shows that 8 moles of \(\mathrm{H}_{2} \mathrm{~S}\) are produced for every 1 mole of \(\mathrm{S}_{8}\). Calculate the moles of \(\mathrm{S}_{8}\) needed:\[Moles\,of\,S_{8} = \frac{0.219}{8} \approx 0.0274 \text{ moles}\]
04

Calculate the Mass of S8 Required

Use the molar mass of \(\mathrm{S}_{8}\) to find the mass required. The molar mass of \(\mathrm{S}_{8}\) (since sulfur has a molar mass of approximately 32.07 g/mol) is:\[Molar\,mass\,of\,S_{8} = 8 \times 32.07 \approx 256.56 \text{ g/mol}\]Calculate the mass:\[Mass\,of\,S_{8} = 0.0274 \times 256.56 \approx 7.03 \text{ grams}\]

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Key Concepts

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

Stoichiometry
Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationship between reactants and products in a chemical reaction. It allows us to calculate amounts of substances, helping determine how much of a reactant is needed or how much product can be formed. In our exercise, stoichiometry was used to connect the moles of hydrogen sulfide gas (\(\text{H}_2\text{S}\)) produced to the moles of sulfur (\(\text{S}_8\)) required. The balanced chemical equation tells us the ratio of how substances react with each other.
  • For every 1 mole of \(\text{S}_8\), 8 moles of \(\text{H}_2\text{S}\) are formed.
  • This ratio (1:8) guides us to calculate the amount of \(\text{S}_8\) needed for a given amount of \(\text{H}_2\text{S}\).
The stoichiometric calculations begin with the balanced equation, ensuring all atoms are conserved. With this understanding, we link the physical measurements (like moles or mass) back to each reactant and product.
Molar Mass
Molar mass connects mass and moles, serving as a bridge between microscopic particles and observable measurements. It tells us the mass of one mole of a given substance, fundamentally based on the mass of each individual atom or molecule in its chemical formula. Consider \(\text{S}_8\) in our exercise:
  • Sulfur (\(\text{S}\)) has a molar mass of approximately 32.07 g/mol.
  • Since \(\text{S}_8\) consists of 8 sulfur atoms, its molar mass is calculated as \(8 \times 32.07 \approx 256.56 \text{ g/mol}\).
Knowing this, you can easily convert moles of \(\text{S}_8\) into grams, or vice versa. For example, if you have 0.0274 moles of \(\text{S}_8\), multiplying by its molar mass gives you the mass: \[\text{Mass of } \text{S}_8 = 0.0274 \times 256.56 \approx 7.03 \text{ grams}\] This conversion is key for practical applications and experimental setups where precise amounts are necessary.
Chemical Reaction
A chemical reaction involves the transformation of reactants into products, often with visible changes such as color, temperature, or state. In the given exercise, the reaction between hydrogen gas (\(\text{H}_2\)) and sulfur (\(\text{S}_8\)) forms hydrogen sulfide gas (\(\text{H}_2\text{S}\)). This reaction is shown by the balanced chemical equation:\[8 \text{H}_2(g) + \text{S}_8(l) \rightarrow 8 \text{H}_2\text{S}(g)\] Key aspects of this type of reaction include:
  • **Reactants:** The starting materials, \(\text{H}_2\) and \(\text{S}_8\), which participate in the chemical process.
  • **Products:** The substances formed as a result, \(\text{H}_2\text{S}\) in this case.
  • **Balanced Equation:** Ensures mass and atoms are conserved during the reaction. Each element has the same number of atoms on both sides of the equation.
Chemical reactions can change the energy and composition of the substances involved, often requiring specific conditions like temperature or pressure to occur, as shown by the high temperature and pressure conditions in our exercise.

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Most popular questions from this chapter

Magnesium burns in air to produce magnesium oxide, \(\mathrm{MgO}\), and magnesium nitride, \(\mathrm{Mg}_{3} \mathrm{~N}_{2}\). Magnesium nitride reacts with water to give ammonia. $$ \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 3 \mathrm{Mg}(\mathrm{OH})_{2}(s)+2 \mathrm{NH}_{3}(g) $$ What volume of ammonia gas at \(24^{\circ} \mathrm{C}\) and \(753 \mathrm{mmHg}\) will be produced from \(4.56 \mathrm{~g}\) of magnesium nitride?

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