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Chapter 7: Problem 3

Determine the molar masses of these compounds: (a) \(\mathrm{NaOH}\) (f) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\) (b) \(\mathrm{Ag}_{2} \mathrm{CO}_{3}\) (g) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (c) \(\mathrm{Cr}_{2} \mathrm{O}_{3}\) (h) \(\mathrm{K}_{4} \mathrm{Fe}(\mathrm{CN})_{6}\) (d) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\) (i) \(\mathrm{BaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (e) \(\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}\)

Short Answer

Expert verified
NaOH = 40.00 g/mol, Ag2CO3 = 275.75 g/mol, Cr2O3 = 152.00 g/mol, (NH4)2CO3 = 96.11 g/mol, Mg(HCO3)2 = 146.34 g/mol, C6H5COOH = 122.13 g/mol, C6H12O6 = 180.18 g/mol, K4Fe(CN)6 = 368.41 g/mol, BaCl2·2H2O = 244.26 g/mol.

Step by step solution

01

Find the Atomic Masses

Look up the atomic masses of each element in the periodic table. For instance, the atomic masses of some key elements are: Na = 22.99, O = 16.00, H = 1.01, Ag = 107.87, C = 12.01, Cr = 52.00, N = 14.01, K = 39.10, Fe = 55.85, Ba = 137.34, Cl = 35.45, Mg = 24.31.
02

Calculate the Molar Mass of \(\text{NaOH}\)

Add the atomic masses of one sodium (Na), one oxygen (O), and one hydrogen (H) atom: NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol.
03

Calculate the Molar Mass of \(\text{Ag}_{2}\text{CO}_{3}\)

Add the atomic masses of two silver (Ag) atoms, one carbon (C) atom, and three oxygen (O) atoms: Ag2CO3 = 2(107.87) + 12.01 + 3(16.00) = 275.75 g/mol.
04

Calculate the Molar Mass of \(\text{Cr}_{2}\text{O}_{3}\)

Add the atomic masses of two chromium (Cr) atoms and three oxygen (O) atoms: Cr2O3 = 2(52.00) + 3(16.00) = 152.00 g/mol.
05

Calculate the Molar Mass of \(\left(\text{NH}_{4}\right)_{2}\text{CO}_{3}\)

Add the atomic masses of two ammonium (NH4) groups and one carbon (C) atom with three oxygen (O) atoms: (NH4)2CO3 = 2(14.01 + 4(1.01)) + 12.01 + 3(16.00) = 96.11 g/mol.
06

Calculate the Molar Mass of \(\text{Mg(HCO}_{3}\text{)}_{2}\)

Add the atomic masses of one magnesium (Mg) atom, two hydrogen (H) atoms, two carbon (C) atoms, and six oxygen (O) atoms: Mg(HCO3)2 = 24.31 + 2(1.01 + 12.01 + 3(16.00)) = 146.34 g/mol.
07

Calculate the Molar Mass of \(\text{C}_{6}\text{H}_{5}\text{COOH}\)

Add the atomic masses of seven carbon (C) atoms, six hydrogen (H) atoms, and two oxygen (O) atoms: C6H5COOH = 7(12.01) + 6(1.01) + 2(16.00) = 122.13 g/mol.
08

Calculate the Molar Mass of \(\text{C}_{6}\text{H}_{12}\text{O}_{6}\)

Add the atomic masses of six carbon (C) atoms, twelve hydrogen (H) atoms, and six oxygen (O) atoms: C6H12O6 = 6(12.01) + 12(1.01) + 6(16.00) = 180.18 g/mol.
09

Calculate the Molar Mass of \(\text{K}_{4}\text{Fe(CN)}_{6}\)

Add the atomic masses of four potassium (K) atoms, one iron (Fe) atom, six carbon (C) atoms, and six nitrogen (N) atoms: K4Fe(CN)6 = 4(39.10) + 55.85 + 6(12.01 + 14.01) = 368.41 g/mol.
10

Calculate the Molar Mass of \(\text{BaCl}_{2}\cdot 2\text{H}_{2}\text{O}\)

Add the atomic masses of one barium (Ba) atom, two chlorine (Cl) atoms, and four hydrogen (H) atoms with two oxygen (O) atoms from water molecules: BaCl2·2H2O = 137.34 + 2(35.45) + 2(2(1.01) + 16.00) = 244.26 g/mol.

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Key Concepts

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

atomic masses
When calculating molar masses, knowing the atomic masses of elements is crucial. Atomic masses are the weights of individual atoms measured in atomic mass units (amu). You can find these values in the periodic table.

For example, sodium (Na) has an atomic mass of 22.99 amu, while oxygen (O) is 16.00 amu. These values are essential to determine the total molar mass of any compound.
  • Use atomic masses to find the weight of each element in a compound.
  • Look these values up in the periodic table for accuracy.
  • Sum the atomic masses for each constituent element to find the molar mass.
periodic table elements
The periodic table is your best friend when it comes to chemistry. It organizes all known elements in a way that allows you to predict many properties, including atomic masses.

Elements are listed in increasing order of their atomic number, which also helps in identifying their atomic masses. Each element’s block contains critical information: the atomic number, symbol, name, and atomic mass.

The periodic table helps you quickly reference the atomic masses needed for molar mass calculations.
compound formulas
Chemical compounds are made up of different elements in specific ratios. The formula of a compound tells you the types and numbers of atoms involved.

For instance, NaOH (sodium hydroxide) consists of one sodium (Na) atom, one oxygen (O) atom, and one hydrogen (H) atom. Understanding the formula is the first step to calculating molar mass.
  • Identify each element in the compound.
  • Note the number of atoms for each element as given in the formula.
  • Use the atomic masses of these elements for your calculations.
step-by-step solution
Approaching molar mass calculations systematically ensures accuracy. Here's a detailed step-by-step method:

  • **Step 1:** Identify the atomic mass of each element in the periodic table.
  • **Step 2:** Write down the compound's formula to see the number of each type of atom.
  • **Step 3:** Multiply the atomic mass by the number of atoms for each element.
  • **Step 4:** Sum these values to get the total molar mass.
This structured approach makes complex calculations simpler and reduces errors.
chemistry education
Understanding how to calculate molar masses is a fundamental skill in chemistry education. It helps students grasp the concept of moles, which is critical for stoichiometry, chemical reactions, and understanding materials' properties.

Chem educators emphasize this topic early on because it's a building block for more advanced concepts. Mastering molar mass calculations leads to better comprehension of chemical quantities and reactions, enabling students to solve real-world chemistry problems effectively.

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Most popular questions from this chapter

For the following compounds whose molecular formulas are given, indicate the empirical formula: (a) \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \quad\) glucose (b) \(\mathrm{C}_{8} \mathrm{H}_{18} \quad\) octane (c) \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3} \quad\) lactic acid (d) \(\mathrm{C}_{25} \mathrm{H}_{52} \quad\) paraffin (e) \(\mathrm{C}_{12} \mathrm{H}_{4} \mathrm{Cl}_{4} \mathrm{O}_{2} \quad\) dioxin (a powerful poison)

\- Vomitoxin is produced by some fungi that grow on wheat and barley. It derives its name from the fact that it causes pigs that eat contaminated wheat to vomit. The chemical formula for vomitoxin is \(\mathrm{C}_{15} \mathrm{H}_{20} \mathrm{O}_{6}\). What is the percent composition of this compound?

The compound \(\mathrm{X}_{2}\left(\mathrm{YZ}_{3}\right)_{3}\) has a molar mass of \(282.23 \mathrm{~g}\) and a percent composition (by mass) of \(19.12 \% \mathrm{X}, 29.86 \% \mathrm{Y}\), and \(51.02 \% \mathrm{Z}\). What is the formula of the compound?

If \(10.0 \mathrm{~g}\) of an unknown compound composed of carbon, hydrogen, and nitrogen contains \(17.7 \% \mathrm{~N}\) and \(3.8 \times 10^{23}\) atoms of hydrogen, what is its empirical formula?

Cosmone is a molecule used by fragrance manufacturers to provide a rich and elegant musky essence to many perfumes. Cosmone has the molecular formula \(\mathrm{C}_{15} \mathrm{H}_{26} \mathrm{O}\). (a) Calculate the molar mass of cosmone. (b) Calculate the mass of \(3.82\) moles of cosmone. (c) Calculate the number of molecules of cosmone in a sample containing \(8.36 \times 10^{-4} \mathrm{~mol}\) cosmone. (d) Calculate the number of moles of carbon in a \(8.35-\mathrm{mol}\) sample of cosmone. (e) Calculate the mass of oxygen in a 4.29-g sample of cosmone. (f) Calculate the mass of a sample of cosmone that contains \(6.58 \times 10^{19}\) atoms of hydrogen. (g) Calculate the mass of one molecule of cosmone. (h) Calculate the number of atoms of carbon in \(8.00-g\) of cosmone.
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