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What is the mass of \(1.00 \mathrm{kmol}\) vitamin \(\mathrm{B} 1\) disulfide \(\mathrm{C}_{24} \mathrm{H}_{34} \mathrm{~N}_{8} \mathrm{O}_{4} \mathrm{~S}_{2}\) ?

Short Answer

Expert verified
The mass of 1.00 kmol Vitamin B1 disulfide, \(\mathrm{C}_{24} \mathrm{H}_{34} \mathrm{N}_{8} \mathrm{O}_{4} \mathrm{S}_{2}\), is approximately the calculated molar mass rounded to the required significant figures, times 1000.

Step by step solution

01

Calculation of Molar Mass

First calculate the molar mass of one mole of the compound using the periodic table values for the atomic masses. Multiply the subscript of each element in the formula by the atomic mass of that element, and then add all these values together. The atomic masses for Carbon (C), Hydrogen (H), Nitrogen (N), Oxygen (O), and Sulfur (S), are approximately 12.01 g/mol, 1.008 g/mol, 14.007 g/mol, 16.00 g/mol, and 32.06 g/mol, respectively. So the molar mass of the compound is: \(24(12.01 \mathrm{g/mol}) + 34(1.008 \mathrm{g/mol}) + 8(14.007 \mathrm{g/mol}) + 4(16.00 \mathrm{g/mol}) + 2(32.06 \mathrm{g/mol})\)
02

Final calculation

Next, you find the mass of one kmol of the substance by multiplying the molar mass by 1000, since one kmol is equal to 1000 moles. The final steps are to evaluate the result and round it to an appropriate number of significant figures.

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Key Concepts

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

Molar Mass Calculation
Calculating the molar mass of a compound is an essential step in understanding its mass per mole. This process begins by identifying each element present in the compound and the number of atoms of that element. Use the chemical formula to find these numbers. For instance, in vitamin B1 disulfide, we observe the formula \(\text{C}_{24} \text{H}_{34} \text{N}_{8} \text{O}_{4} \text{S}_{2}\). This tells us:
  • 24 Carbon (C) atoms
  • 34 Hydrogen (H) atoms
  • 8 Nitrogen (N) atoms
  • 4 Oxygen (O) atoms
  • 2 Sulfur (S) atoms
Next, utilize the atomic masses of these elements:
  • Carbon: 12.01 g/mol
  • Hydrogen: 1.008 g/mol
  • Nitrogen: 14.007 g/mol
  • Oxygen: 16.00 g/mol
  • Sulfur: 32.06 g/mol
Multiply the atomic mass of each element by the number of atoms indicated in the formula:
  • Carbon: \(24 \times 12.01 = 288.24 \; \text{g/mol}\)
  • Hydrogen: \(34 \times 1.008 = 34.272 \; \text{g/mol}\)
  • Nitrogen: \(8 \times 14.007 = 112.056 \; \text{g/mol}\)
  • Oxygen: \(4 \times 16.00 = 64.00 \; \text{g/mol}\)
  • Sulfur: \(2 \times 32.06 = 64.12 \; \text{g/mol}\)
Finally, sum these values to determine the molar mass of the compound: \[ 288.24 + 34.272 + 112.056 + 64.00 + 64.12 = 562.688 \; \text{g/mol} \] The result, 562.688 g/mol, is the molar mass of vitamin B1 disulfide.
Stoichiometry
Stoichiometry is a fundamental concept in chemical engineering, allowing us to make quantitative predictions about chemical reactions. It involves tasks like balancing chemical equations and converting between units such as moles, grams, and molecules.
In practice, stoichiometry is used to determine how much reactant is needed to produce a desired amount of product or to predict how much product will be made from given reactants. This process begins with a balanced chemical equation, which serves as a mathematical model for the chemical reaction.
Consider the task of finding the mass of a kmol of vitamin B1 disulfide. Stoichiometry gives us the step-by-step conversion from kmol to grams, enabling precise measurements crucial for large-scale production processes in chemical engineering. Remember, 1 kilomole (kmol) equals 1000 moles, making it simple to scale up from laboratory experiments to industrial applications.
By understanding stoichiometry, chemical engineers can optimize reactions, improve efficiency, and reduce waste, all of which are key in designing sustainable industrial processes.
Chemical Formulas
Chemical formulas are the language of chemistry, providing concise information about the composition of compounds. They indicate the elements present and the ratio of atoms involved. For complex compounds like vitamin B1 disulfide, the formula \(\text{C}_{24} \text{H}_{34} \text{N}_{8} \text{O}_{4} \text{S}_{2}\) reveals the intricacies in its composition.
To thoroughly comprehend a chemical formula, it's crucial to understand the basics:
  • Subscripts: Specify the number of each type of atom in the molecule. For example, the 24 in \(\text{C}_{24}\) means there are 24 carbon atoms.
  • Coefficients: When present, they indicate how many molecules or moles of the entire formula are involved, though not needed in this specific exercise.
Knowledge of chemical formulas aids in calculating molar masses and understanding stoichiometry by providing the blueprint of the compound's structure. Working with formulas involves balancing proportions to leverage the atomic masses of elements to find answers like those in molar mass calculations. Making sense of these formulas is a critical skill in chemical engineering, ensuring the precision needed for chemical synthesis and analysis.
Atomic Mass
Atomic mass is a measure of the mass of an individual atom. It is usually expressed in atomic mass units (amu), where 1 amu is equivalent to one-twelfth of the mass of a carbon-12 atom, the standard for measuring atomic masses. Understanding atomic mass is foundational for calculating molar masses.
For instance, to find the atomic masses of elements in vitamin B1 disulfide, you refer to the periodic table:
  • Carbon has an atomic mass of approximately 12.01 amu.
  • Hydrogen's atomic mass is about 1.008 amu.
  • Nitrogen weighs in at about 14.007 amu.
  • Oxygen has an atomic mass of roughly 16.00 amu.
  • Lastly, Sulfur's atomic mass is around 32.06 amu.
These values are crucial as they serve as the basis for further calculations. Multiplying atomic mass by the number of atoms helps determine the contribution of each element to the total molar mass of a compound. This understanding is essential for computing stoichiometric amounts and analyzing chemical reactions, which are fundamental aspects of chemical engineering.

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Most popular questions from this chapter

A gallon of gasoline has a mass of about \(3.0 \mathrm{~kg}\). Further, a \(\mathrm{kg}\) of gasoline has an energy content of about \(45,500 \mathrm{~kJ} / \mathrm{kg}\). If an experimental automobile requires just 10 . kW of power to overcome air resistance at steady speed of 30 . miles an hour, and if there are no other losses, what would the gas mileage of the car be in miles per gallon? (Ans. 110 mpg to only two significant figures, as problem is stated.)

The effective molecular mass of air is defined as the mass of a kmol of elementary particles of which \(78.09 \%\) are nitrogen molecules, \(20.95 \%\) are oxygen molecules, \(0.933 \%\) are argon atoms, and \(0.027 \%\) are carbon dioxide molecules. What is the effective molecular mass of air? (Watch your significant figures!) What other factor could affect the effective molecular mass of air?

It is 2021 , and you are a process engineer at a large oil refining company. The world is rapidly moving toward a hydrogen energy economy, and your company has been trying to develop an efficient and cost-effective way to extract hydrogen from crude oil. You found a low-cost process, but it produces a considerable amount of undesirable chemical by-product pollutants. However, during your work on this project, you also discovered an effective and inexpensive way to extract hydrogen directly from seawater. You realize that revealing this process would effectively eliminate the world demand for petroleum and would probably cause serious financial damage to your company. What do you do? (Give your solution using the Engineering Ethics Matrix.) a. Quit your job and start your own hydrogen producing company. b. Talk to your supervisors and reveal your process to them to see if they wish to pursue implementing it as part of their company. C. Contact a patent lawyer not associated with your current employer and try to patent this potentially lucrative new process. d. Without your employer's permission, publish an article in a well-read chemical or energy magazine revealing your process and giving it to the world free of charge.

Determine the mass air-to-fuel ratio \((A / F)_{\text {mass }}\) for the combustion of isooctane \(\mathrm{C}_{8} \mathrm{H}_{18}\) in air. Its stoichiometric equation is $$ \mathrm{C}_{8} \mathrm{H}_{18}+12.5\left(\mathrm{O}_{2}+3.76 \mathrm{~N}_{2}\right)=8 \mathrm{CO}_{2}+9 \mathrm{H}_{2} \mathrm{O}+47.0 \mathrm{~N}_{2} \text {. } $$ Exercises 15-20 use engineering considerations to give insight on the "global warming" issue.

Determine the value of the stoichiometric coefficients for the combustion of natural gas in air: $$ \mathrm{CH}_{4}+a\left(\mathrm{O}_{2}+3.76 \mathrm{~N}_{2}\right)=b \mathrm{CO}_{2}+c \mathrm{H}_{2} \mathrm{O}+d \mathrm{~N}_{2} $$

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