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Calculate the number of moles of sulfur atoms present in each of the following samples. a. \(2.01 \mathrm{~g}\) of sodium sulfate b. \(2.01 \mathrm{~g}\) of sodium sulfite c. \(2.01 \mathrm{~g}\) of sodium sulfide d. \(2.01 \mathrm{~g}\) of sodium thiosulfate, \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\)

Short Answer

Expert verified
The number of moles of sulfur atoms present in each sodium compound is as follows: a. Sodium sulfate: \(0.0141\,\mathrm{mol}\) of sulfur atoms b. Sodium sulfite: \(0.0159\,\mathrm{mol}\) of sulfur atoms c. Sodium sulfide: \(0.0258\,\mathrm{mol}\) of sulfur atoms d. Sodium thiosulfate: \(0.0254\,\mathrm{mol}\) of sulfur atoms

Step by step solution

01

Find molecular weights of the compounds

First, we need to find the molecular weight of each sodium compound using the atomic weight of Sodium, Sulfur, and Oxygen. a. Sodium sulfate (\(Na_{2}SO_{4}\)): \(2 * 22.99\,\mathrm{(Na)} + 32.07\,\mathrm{(S)} + 4 * 16.00\,\mathrm{(O)}=142.05\,\mathrm{g/mol}\) b. Sodium sulfite (\(Na_{2}SO_{3}\)): \(2 * 22.99\,\mathrm{(Na)} + 32.07\,\mathrm{(S)} + 3 * 16.00\,\mathrm{(O)} = 126.05\,\mathrm{g/mol}\) c. Sodium sulfide (\(Na_{2}S\)): \(2 * 22.99\,\mathrm{(Na)} + 32.07\,\mathrm{(S)} = 78.05\,\mathrm{g/mol}\) d. Sodium thiosulfate (\(Na_{2}S_{2}O_{3}\)): \(2 * 22.99\,\mathrm{(Na)} + 2 * 32.07\,\mathrm{(S)} + 3 * 16.00\,\mathrm{(O)} = 158.11\,\mathrm{g/mol}\)
02

Calculate moles of the compounds

Next, we need to calculate the moles of each compound by dividing the given mass by the molecular weight of the respective compound. a. moles of \(Na_{2}SO_{4}\): \(\frac{2.01\,\mathrm{g}}{142.05\,\mathrm{g/mol}} = 0.0141\,\mathrm{mol}\) b. moles of \(Na_{2}SO_{3}\): \(\frac{2.01\,\mathrm{g}}{126.05\,\mathrm{g/mol}} = 0.0159\,\mathrm{mol}\) c. moles of \(Na_{2}S\): \(\frac{2.01\,\mathrm{g}}{78.05\,\mathrm{g/mol}} = 0.0258\,\mathrm{mol}\) d. moles of \(Na_{2}S_{2}O_{3}\): \(\frac{2.01\,\mathrm{g}}{158.11\,\mathrm{g/mol}} = 0.0127\,\mathrm{mol}\)
03

Calculate moles of sulfur atoms

Next, we need to calculate the moles of sulfur atoms present in each compound. a. moles of sulfur in \(Na_{2}SO_{4}\): 1 sulfur atom in one molecule, so \(0.0141\,\mathrm{mol}\) of sulfur atoms. b. moles of sulfur in \(Na_{2}SO_{3}\): 1 sulfur atom in one molecule, so \(0.0159\,\mathrm{mol}\) of sulfur atoms. c. moles of sulfur in \(Na_{2}S\): 1 sulfur atom in one molecule, so \(0.0258\,\mathrm{mol}\) of sulfur atoms. d. moles of sulfur in \(Na_{2}S_{2}O_{3}\): 2 sulfur atoms in one molecule, so \(2 * 0.0127\,\mathrm{mol}\) = \(0.0254\,\mathrm{mol}\) of sulfur atoms.
04

Final Answer

Now we have calculated the number of moles of sulfur atoms present in each sodium compound: a. Sodium sulfate: \(0.0141\,\mathrm{mol}\) of sulfur atoms b. Sodium sulfite: \(0.0159\,\mathrm{mol}\) of sulfur atoms c. Sodium sulfide: \(0.0258\,\mathrm{mol}\) of sulfur atoms d. Sodium thiosulfate: \(0.0254\,\mathrm{mol}\) of sulfur atoms

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Key Concepts

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

Molecular Weight
Molecular weight is an essential concept in chemistry, which aids in the conversion between mass and moles of a chemical compound. The molecular weight, also known as molecular mass, is the sum of the atomic weights of all the atoms in a molecule. For instance, let's take sodium sulfate, which has a chemical formula of \(Na_2SO_4\). To calculate its molecular weight, we take the atomic weight of sodium (\(Na\)), which is \(22.99\,\mathrm{g/mol}\), multiplied by 2, since there are two sodium atoms. Then, we add the atomic weight of sulfur (\(S\)), \(32.07\,\mathrm{g/mol}\), and four times the atomic weight of oxygen (\(O\)), \(16.00\,\mathrm{g/mol}\). This results in \(142.05\,\mathrm{g/mol}\) for sodium sulfate. Such calculations are crucial for accurate mole calculations, which are used in many chemical experiments and reactions. Understanding this helps you see the connection between mass measurements and mole-based calculations.
Sulfur Atoms
Sulfur atoms are a significant element in many chemical compounds, especially those used in industrial and laboratory settings. To determine the number of moles of sulfur atoms in a compound, you need to first find out how many sulfur atoms are present in the formula unit of the compound. For example, in sodium sulfate (\(Na_2SO_4\)), there is one sulfur atom per molecule. Meanwhile, in sodium thiosulfate (\(Na_2S_2O_3\)), there are two sulfur atoms per molecule. To find the moles of sulfur, multiply the moles of the compound by the number of sulfur atoms per formula. This means, if you have \(0.0127\,\mathrm{mol}\) of sodium thiosulfate, you will have \(2 * 0.0127 = 0.0254\,\mathrm{mol}\) of sulfur atoms. Understanding this concept ensures you can accurately calculate and balance chemical reactions where sulfur is involved.
Chemical Compounds
Chemical compounds are substances composed of two or more different elements that are chemically bonded together. The examples provided - sodium sulfate, sodium sulfite, sodium sulfide, and sodium thiosulfate - each contain sulfur and are bonded with sodium and, in most cases, oxygen as well. These compounds show the diversity in chemical bonding and composition. Chemical formulas provide the proportion of each type of atom in the compound. For example, \(Na_2SO_4\) indicates two sodium atoms, one sulfur atom, and four oxygen atoms per molecule. This information is invaluable for stoichiometry calculations, which rely heavily on understanding the ratios in which elements are combined. Recognizing these formulas helps one to conceptualize the quantities of individual atoms, such as sulfur, within larger compounds.
Stoichiometry
Stoichiometry is a branch of chemistry concerned with the quantification of the relationships between reactants and products in a chemical reaction. It involves using balanced chemical equations alongside mole concepts to predict the outcome of reactions in terms of masses, volumes, and moles. One must be adept at working with chemical formulas and equations to solve stoichiometric problems, which often involve steps like determining moles of a substance, just as done in the sulfur atom calculation. To apply stoichiometry, you start by writing the balanced chemical equation for the reaction. From here, use the mole ratios derived from the equation to determine how much of each substance is required or produced. In the problem given, calculating the moles of sulfur atoms in the sodium compounds is an application of stoichiometry principles. With these calculations, you establish a relationship between the compound's mass, its molecular weight, and its constituent atoms, ensuring precise chemical computations.

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