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Chapter 3: Problem 69

What number of atoms of nitrogen are present in 5.00 g of each of the following? \(\begin{array}{ll}{\text { a. glycine, } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{N}} & {\text { c. calcium nitrate }} \\ {\text { b. magnesium nitride }} & {\text { d. dinitrogen tetroxide }}\end{array}\)

Short Answer

Expert verified
In 5.00g of each compound, the number of nitrogen atoms is as follows: a. Glycine: \(4.01 脳 10^{22}\, atoms\, N\) b. Magnesium Nitride: \(5.96 脳 10^{22}\, atoms\, N\) c. Calcium Nitrate: \(3.67 脳 10^{22}\, atoms\, N\) d. Dinitrogen Tetroxide: \(6.54 脳 10^{22}\, atoms\, N\)

Step by step solution

01

Determine the molar mass of each compound

Molar mass of: a. Glycine, \(C_2H_5O_2N\): (2 脳 12.01)g/mol + (5 脳 1.01)g/mol + (2 脳 16.00)g/mol + 14.01g/mol = 75.07 g/mol b. Magnesium Nitride, \(Mg_3N_2\): (3 脳 24.31)g/mol + (2 脳 14.01)g/mol = 100.95 g/mol c. Calcium Nitrate, \(Ca(NO_3)_2\): 40.08g/mol + 2 脳 (14.01g/mol + 3 脳 16.00g/mol) = 164.10 g/mol d. Dinitrogen Tetroxide, \(N_2O_4\): (2 脳 14.01)g/mol + (4 脳 16.00)g/mol = 92.02 g/mol
02

Convert grams to moles using the molar mass of the compound

a. \(5.00 \,g\, C_2H_5O_2N 脳 \frac{1\, mol C_2H_5O_2N}{75.07\,g\, C_2H_5O_2N} = 0.0666\, mol\, C_2H_5O_2N\) b. \(5.00 \,g\, Mg_3N_2 脳 \frac{1\, mol Mg_3N_2}{100.95\,g\, Mg_3N_2} = 0.0495\, mol\, Mg_3N_2\) c. \(5.00 \,g\, Ca(NO_3)_2 脳 \frac{1\, mol \,Ca(NO_3)_2}{164.10\,g\, Ca(NO_3)_2} = 0.0305\, mol\, Ca(NO_3)_2\) d. \(5.00 \,g\, N_2O_4 脳 \frac{1\, mol \,N_2O_4}{92.02\,g\, N_2O_4} = 0.0543\, mol\, N_2O_4\)
03

Find the mole-to-atom ratio of nitrogen in each compound

a. In Glycine, 1 mole of Glycine (\(C_2H_5O_2N\)) contains 1 mole of Nitrogen b. In Magnesium Nitride, 1 mole of Magnesium Nitride (\(Mg_3N_2\)) contains 2 moles of Nitrogen c. In Calcium Nitrate, 1 mole of Calcium Nitrate (\(Ca(NO_3)_2\)) contains 2 moles of Nitrogen d. In Dinitrogen Tetroxide, 1 mole of Dinitrogen Tetroxide (\(N_2O_4\)) contains 2 moles of Nitrogen
04

Calculate the number of nitrogen atoms using the mole-to-atom ratio

a. \(0.0666\, mol\, C_2H_5O_2N 脳 \frac{1\, mol\, N}{1\, mol\, C_2H_5O_2N} = 0.0666\, mol\, N\) b. \(0.0495\, mol\, Mg_3N_2 脳 \frac{2\, mol\, N}{1\, mol\, Mg_3N_2} = 0.0990\, mol\, N\) c. \(0.0305\, mol\, Ca(NO_3)_2 脳 \frac{2\, mol\, N}{1\, mol\, Ca(NO_3)_2} = 0.0610\, mol\, N\) d. \(0.0543\, mol\, N_2O_4 脳 \frac{2\, mol\, N}{1\, mol\, N_2O_4} = 0.1086\, mol\, N\) Now, we convert moles of Nitrogen to the number of atoms using Avogadro's number: \(1\, mol\, N = 6.022 脳 10^{23}\, atoms\, N\) a. \(0.0666\, mol\, N 脳 6.022 脳 10^{23}\, atoms\, N/mol = 4.01 脳 10^{22}\, atoms\, N\) b. \(0.0990\, mol\, N 脳 6.022 脳 10^{23}\, atoms\, N/mol = 5.96 脳 10^{22}\, atoms\, N\) c. \(0.0610\, mol\, N 脳 6.022 脳 10^{23}\, atoms\, N/mol = 3.67 脳 10^{22}\,atoms\, N\) d. \(0.1086\, mol\, N 脳 6.022 脳 10^{23}\, atoms\, N/mol = 6.54 脳 10^{22}\, atoms\, N\) In conclusion, the number of nitrogen atoms in \(5.00 \,g\) of each compound is: a. Glycine: \(4.01 脳 10^{22}\, atoms\, N\) b. Magnesium Nitride: \(5.96 脳 10^{22}\, atoms\, N\) c. Calcium Nitrate: \(3.67 脳 10^{22}\, atoms\, N\) d. Dinitrogen Tetroxide: \(6.54 脳 10^{22}\, atoms\, N\)

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Key Concepts

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

Molar Mass
The molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). Calculating the molar mass of a compound involves adding up the atomic masses of all the atoms in its chemical formula. For instance, in glycine (\( C_2H_5O_2N \)), you multiply the number of each type of atom by its atomic weight:
  • Carbon (C) has an atomic weight of 12.01 g/mol and there are 2 carbon atoms, so \( 2 \times 12.01 \) g/mol.
  • Hydrogen (H) has an atomic weight of 1.01 g/mol, with 5 hydrogen atoms, it becomes \( 5 \times 1.01 \) g/mol.
  • Oxygen (O) has an atomic weight of 16.00 g/mol and there are 2 atoms, yielding \( 2 \times 16.00 \) g/mol.
  • Nitrogen (N) has an atomic weight of 14.01 g/mol, contributing \( 1 \times 14.01 \) g/mol.
By adding these up, you can determine the molar mass of glycine as 75.07 g/mol. Understanding the molar mass is crucial for converting a substance's mass to moles, which is a key step in stoichiometry.
Avogadro's Number
Avogadro's number is a fundamental constant in chemistry that defines the number of entities, usually atoms or molecules, in one mole of a substance. It is quantified as approximately \( 6.022 \times 10^{23} \). This number allows chemists to translate between the macroscopic scale of materials we can measure and the microscopic scale of atoms and molecules. For instance, when you have one mole of nitrogen atoms, you actually have \( 6.022 \times 10^{23} \) nitrogen atoms. This greatly simplifies calculations for chemical reactions and helps in converting between moles and the number of atoms, which is an essential step when dealing with stoichiometry problems. By employing Avogadro's number, one can determine how many atoms or molecules are present in a given mole of a substance.
Mole-to-Atom Conversion
Mole-to-atom conversion is an essential process in chemistry that allows us to determine the actual number of atoms in a given amount of substance, measured in moles. The conversion is achieved through the use of Avogadro's number. For example, in the problem provided, once we have calculated the moles of nitrogen from various compounds, we can convert these moles into atoms by multiplying by Avogadro's number: - If you have \( 0.0666 \) moles of nitrogen from glycine, you multiply \( 0.0666 \) by \( 6.022 \times 10^{23} \) to get \( 4.01 \times 10^{22} \) atoms of nitrogen.This conversion gives you a practical count of how many nitrogen atoms are present, which is critical in deeper chemical analysis and understanding reactions.
Number of Atoms
The number of atoms in a sample gives insight into how substances interact chemically. Once you have the number of moles, calculating the number of atoms involves using both the mole-to-atom conversion and Avogadro's number.Consider dinitrogen tetroxide (\( N_2O_4 \)):
  • Convert its mass in grams to moles.
  • Recognize that one mole of \( N_2O_4 \) contains two moles of nitrogen atoms due to its chemical structure.
  • Use Avogadro's number to convert moles to atoms. For \( 0.1086 \) moles of nitrogen, multiply by \( 6.022 \times 10^{23} \) to result in \( 6.54 \times 10^{22} \) nitrogen atoms.
Understanding the concept of the number of atoms helps to fathom the scale of atomic particles in measurable amounts of a compound, enabling chemists to predict how substances will behave in chemical reactions.

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Most popular questions from this chapter

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