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Chapter 2: Problem 107

Give the number of atoms of the specified element in a formula unit of each of the following compounds, and calculate the molecular (formula) mass: (a) Oxygen in aluminum sulfate, \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (b) Hydrogen in ammonium hydrogen phosphate, \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) (c) Oxygen in the mineral azurite, \(\mathrm{Cu}_{3}(\mathrm{OH})_{2}\left(\mathrm{CO}_{3}\right)_{2}\)

Short Answer

Expert verified
a) 12 atoms, 342.17 u; b) 9 atoms, 133.062 u; c) 8 atoms, 344.686 u

Step by step solution

01

- Identify the number of atoms of the specified element in the compound

(a) For \(\text{Al}_2(\text{SO}_4)_3\): \ \Each \(\text{SO}_4\) molecule contains 4 oxygen atoms. Since there are 3 \(\text{SO}_4\) molecules, the total number of oxygen atoms is \(4 \times 3 = 12\).
02

- Identify the number of atoms of the specified element in the compound

(b) For \( (\text{NH}_4)_2\text{HPO}_4 \): \ \Each \( \text{NH}_4 \) contains 1 hydrogen atom. Since there are 2 \( \text{NH}_4 \) molecules, there are \(2 \times 4 = 8 \) hydrogen atoms from \( \text{NH}_4 \). Additionally, there is 1 more hydrogen atom in \(\text{HPO}_4\). Therefore, the total number of hydrogen atoms is \(8 + 1 = 9\).
03

- Identify the number of atoms of the specified element in the compound

(c) For \( \text{Cu}_3(\text{OH})_2(\text{CO}_3)_2 \): \ \Each \( \text{OH} \) contains 1 oxygen atom. Since there are 2 \( \text{OH} \) molecules, there are \(2 \) oxygen atoms from \( \text{OH} \). Similarly, each \( \text{CO}_3 \) molecule contains 3 oxygen atoms. Since there are 2 \( \text{CO}_3 \) molecules, there are \(2 \times 3 = 6 \) oxygen atoms from \( \text{CO}_3 \). Therefore, the total number of oxygen atoms is \(2 + 6 = 8\).
04

- Calculate molecular (formula) mass

(a) For \(\text{Al}_2(\text{SO}_4)_3\): \ \Molecular mass = 2(Mass of Al) + 3[ \( \text{Mass of S + 4(Mass of O)} \)] \ \= 2(26.98) + 3[ \( 32.07 + 4(16.00) \)] \ \= 2(26.98) + 3[32.07 + 64.00] = 2(26.98) + 3[96.07] \ \= 53.96 + 288.21 = 342.17 \ \Thus, the molecular mass is 342.17 u.
05

- Calculate molecular (formula) mass

(b) For \( (\text{NH}_4)_2\text{HPO}_4 \): \ \Molecular mass = 2[ \( 14.01 + 4(1.008) \)] + [ \( 1.008 + 31.97 + 4(16.00) \)] \ \= 2[14.01 + 4.032] + [1.008 + 31.97 + 64] = 2[18.042] + 96.978 \ \= 36.084 + 96.978 = 133.062 \ \Thus, the molecular mass is 133.062 u.
06

- Calculate molecular (formula) mass

(c) For \( \text{Cu}_3(\text{OH})_2(\text{CO}_3)_2 \): \ \Molecular mass = 3(Mass of Cu) + 2[ \( 1.008 + 16.00 \)] + 2[ \( 12.01 + 3(16.00) \)] \ \= 3(63.55) + 2[17.008] + 2[60.01] \ \= 190.65 + 34.016 + 120.02 = 344.686 \ \Thus, the molecular mass is 344.686 u.

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Key Concepts

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

Chemical Formula Composition
Understanding the chemical formula of a compound is essential in chemistry. Every chemical formula, like \( \text{Al}_2(\text{SO}_4)_3 \), \( (\text{NH}_4)_2\text{HPO}_4 \), and \( \text{Cu}_3(\text{OH})_2(\text{CO}_3)_2 \), represents the specific ratio of atoms of each element in the compound.
For example:
  • \( \text{Al}_2(\text{SO}_4)_3 \) tells us there are 2 aluminum (Al) atoms and 3 sulfate (SO₄) units in one formula unit.
  • \( (\text{NH}_4)_2\text{HPO}_4 \) indicates 2 ammonium (NH₄) groups and 1 hydrogen phosphate (HPO₄).
  • \( \text{Cu}_3(\text{OH})_2(\text{CO}_3)_2 \) shows 3 copper (Cu), 2 hydroxide (OH), and 2 carbonate (CO₃) groups.
This understanding helps in accurately determining the number of each type of atom in a molecule and in further calculations such as determining molecular mass.
Atom Count in Compounds
Counting the atoms of each element in a compound is a fundamental step in chemistry. Let's take some examples to understand it better:
In \( \text{Al}_2(\text{SO}_4)_3 \), each sulfate (SO₄) group contains 4 oxygen atoms. With 3 sulfate groups in the compound, the total number of oxygen atoms is \( 4 \times 3 = 12 \).
  • For \( (\text{NH}_4)_2\text{HPO}_4 \), each ammonium (NH₄) group has 4 hydrogen atoms. Since there are 2 ammonium groups, they contribute \( 2 \times 4 = 8 \) hydrogen atoms. Adding the single hydrogen in HPO₄, the total hydrogen count becomes \( 8 + 1 = 9 \).
  • In \( \text{Cu}_3(\text{OH})_2(\text{CO}_3)_2 \), each hydroxide (OH) group has 1 oxygen atom. With 2 such groups, there are \( 2 \) oxygen atoms. Each carbonate (CO₃) group has 3 oxygen atoms, and with 2 such groups, this contributes \( 2 \times 3 = 6 \) oxygen atoms. The total number of oxygen atoms is \( 2 + 6 = 8 \).
Practicing these calculations helps you develop a strong foundation for understanding and working with chemical formulas.
Molecular Mass Determination
Calculating the molecular mass of a compound involves summing the atomic masses of all atoms in the compound. Here's how you can do it step by step:
  • For \( \text{Al}_2(\text{SO}_4)_3 \):
    The atomic mass of Al (aluminum) is 26.98 u. So, with 2 Al atoms, the total mass contribution from Al is \( 2 \times 26.98 = 53.96 \) u.
    Each SO₄ group has 1 sulfur (S) and 4 oxygens (O). The atomic masses are 32.07 u for S and 16.00 u for O. So, the mass of one SO₄ is \( 32.07 + 4 \times 16.00 = 96.07 \) u.
    With 3 SO₄ groups, the mass is \( 3 \times 96.07 = 288.21 \) u.
    Therefore, the total molecular mass is \( 53.96 + 288.21 = 342.17 \) u.
  • For \( (\text{NH}_4)_2\text{HPO}_4 \):
    The mass contribution from 2 NH₄ groups is \( 2 \times [14.01 + 4 \times 1.008] = 2 \times 18.042 = 36.084 \) u.
    The mass from HPO₄ is \( 1.008 + 31.97 + 4 \times 16.00 = 96.978 \) u.
    Therefore, the total molecular mass is \( 36.084 + 96.978 = 133.062 \) u.
  • For \( \text{Cu}_3(\text{OH})_2(\text{CO}_3)_2 \):
    The mass contribution from 3 Cu atoms is \( 3 \times 63.55 = 190.65 \) u.
    From 2 OH groups, it is \( 2 \times (1.008 + 16.00) = 34.016 \) u.
    From 2 CO₃ groups, it is \( 2 \times (12.01 + 3 \times 16.00) = 120.02 \) u.
    Therefore, the total molecular mass is \( 190.65 + 34.016 + 120.02 = 344.686 \) u.
Mastering these calculations will help you understand the composition and quantitative aspects of chemical compounds better.

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Most popular questions from this chapter

List two differences between a compound and a mixture.

Correct each of the following names: (a) CuI is cobalt(II) iodide. (b) \(\mathrm{Fe}\left(\mathrm{HSO}_{4}\right)_{3}\) is iron(II) sulfate. (c) \(\mathrm{MgCr}_{2} \mathrm{O}_{7}\) is magnesium dichromium heptaoxide. (d) \(\mathrm{CaCl}_{2}\) is calcium(II) dichloride.

(a) Does the percent by mass of each element in a compound depend on the amount of compound? Explain. (b) Does the mass of each element in a compound depend on the amount of compound? Explain.

State the mass law(s) demonstrated by the following experimental results, and explain your reasoning: Experiment 1: A student heats \(1.00 \mathrm{~g}\) of a blue compound and obtains \(0.64 \mathrm{~g}\) of a white compound and \(0.36 \mathrm{~g}\) of a colorless gas. Experiment 2: A second student heats \(3.25 \mathrm{~g}\) of the same blue compound and obtains \(2.08 \mathrm{~g}\) of a white compound and \(1.17 \mathrm{~g}\) of a colorless gas.

Argon has three naturally occurring isotopes, \({ }^{36} \mathrm{Ar},{ }^{38} \mathrm{Ar}\) and \({ }^{40}\) Ar. What is the mass number of each isotope? How many protons, neutrons, and electrons are present in each?
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