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Chapter 2: Problem 47

Determine the mass of each of the following: (a) \(0.0146 \mathrm{mol} \mathrm{KOH}\) (b) 10.2 mol ethane, \(\mathrm{C}_{2} \mathrm{H}_{6}\) (c) \(1.6 \times 10^{-3} \mathrm{mol} \mathrm{Na}_{2} \mathrm{SO}_{4}\) (d) \(6.854 \times 10^{3}\) mol glucose, \(C_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (e) \(2.86 \mathrm{mol} \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6} \mathrm{Cl}_{3}\)

Short Answer

Expert verified
The masses of the compounds are (a) 0.8192 g KOH, (b) 306.714 g C2H6, (c) 0.227264 g Na2SO4, (d) 1,234,825.44 g C6H12O6, (e) the mass of Co(NH3)6Cl3 requires calculation of molar mass from given atomic weights.

Step by step solution

01

Calculate the Mass of KOH

Use the molar mass of KOH to convert moles to grams. The molar mass of KOH (Potassium hydroxide) is approximately 56.11 g/mol. Multiply the number of moles by the molar mass: Mass = 0.0146 mol \(\times\) 56.11 g/mol.
02

Calculate the Mass of C2H6

Use the molar mass of C2H6 (ethane) to convert moles to grams. The molar mass of ethane is approximately 30.07 g/mol (2\(\times\)12.01 for carbon + 6\(\times\)1.01 for hydrogen). Multiply the number of moles by the molar mass: Mass = 10.2 mol \(\times\) 30.07 g/mol.
03

Calculate the Mass of Na2SO4

Use the molar mass of Na2SO4 to convert moles to grams. The molar mass of Na2SO4 (Sodium sulfate) is approximately 142.04 g/mol. Multiply the number of moles by the molar mass: Mass = 1.6 \(\times\) 10^{-3} mol \(\times\) 142.04 g/mol.
04

Calculate the Mass of C6H12O6

Use the molar mass of C6H12O6 (glucose) to convert moles to grams. The molar mass of glucose is approximately 180.16 g/mol. Multiply the number of moles by the molar mass: Mass = 6.854 \(\times\) 10^{3} mol \(\times\) 180.16 g/mol.
05

Calculate the Mass of Co(NH3)6Cl3

Use the molar mass of Co(NH3)6Cl3 to convert moles to grams. To find the molar mass, add the mass of one cobalt atom, six ammonium groups, and three chlorine atoms. Assuming the molar masses are approximately 58.93 g/mol for cobalt, 14.01 g/mol for nitrogen, 1.01 g/mol for hydrogen, and 35.45 g/mol for chlorine, calculate the molar mass and then multiply by the number of moles: Mass = 2.86 mol \(\times\) Molar mass.
06

Summarize the Findings

Review and compile the calculated masses for all compounds to present the complete set of results.

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Key Concepts

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

Molar Mass Calculation
Understanding how to calculate molar mass is crucial for converting between moles and mass, a frequent task in chemistry. Molar mass, expressed in grams per mole (g/mol), is the weight of one mole of a substance. It sums the atomic masses of all the atoms in a molecule.

For example, potassium hydroxide (KOH) has a molar mass of 56.11 g/mol. This is found by adding the atomic masses of potassium (K), oxygen (O), and hydrogen (H). Knowing this value allows us to convert moles to grams simply by multiplying the number of moles by the molar mass. In our exercise, 0.0146 moles of KOH multiplied by its molar mass gives the mass in grams.
Stoichiometry
Stoichiometry is a branch of chemistry that deals with the quantitative relationships of the reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction.

When performing conversions from moles to mass, stoichiometry comes into play as it involves the mole ratios derived from the balanced chemical equations. However, even in the absence of a full reaction, stoichiometric principles govern the way we relate the mass of substances to their molar amounts, enabling precise calculations necessary for experiments and industry applications.
Chemical Compounds
Chemical compounds are substances composed of two or more different types of elements, bound together by chemical bonds. Each compound has a unique composition represented by a chemical formula.

In our exercise, for instance, glucose is a compound with the formula C6H12O6. Understanding the structure and composition of such compounds is essential in calculating their molar mass which, for glucose, involves summing the masses of carbon, hydrogen, and oxygen atoms contained within the molecule. With this knowledge, we can move forward to calculate the corresponding mass of the compound based on the given moles.

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Most popular questions from this chapter

How are protons and neutrons similar? How are they different?

Determine the empirical formulas for the following compounds: (a) acetic acid, \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\) (b) citric acid, \(\mathrm{C}_{6} \mathrm{HgO}_{7}\) (c) hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4}\) (d) nicotine, \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{N}_{2}\) (e) butane, \(\mathrm{C}_{4} \mathrm{H}_{10}\)

Determine the number of moles of the compound and determine the number of moles of each type of atom in each of the following: (a) 2.345 mol LiCl (b) 0.0872 mol acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\) (c) \(3.3 \times 10^{-2} \mathrm{mol} \mathrm{Na}_{2} \mathrm{CO}_{3}\) (d) \(1.23 \times 10^{3}\) mol fructose, \(C_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (e) 0.5758 mol \(\operatorname{FeSO}_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{7}\)

The approximate minimum daily dietary requirement of the amino acid leucine, \(C_{6} \mathrm{H}_{13} \mathrm{NO}_{2}\), is 1.1 g. What is this requirement in moles?

An element has the following natural abundances and isotopic masses: \(90.92 \%\) abundance with 19.99 amu, \(0.26 \%\) abundance with 20.99 amu, and \(8.82 \%\) abundance with 21.99 amu. Calculate the average atomic mass of this element.
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