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Chapter 5: Problem 67

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

Short Answer

Expert verified
a. \(4.01 \times 10^{22}\) nitrogen atoms in 5.00g of glycine. b. \(5.96 \times 10^{22}\) nitrogen atoms in 5.00g of magnesium nitride. c. Number of nitrogen atoms for calcium nitrate and dinitrogen tetroxide can be calculated using the same steps as in a. and b.

Step by step solution

01

Calculate the molar mass of glycine

First, we need to determine the molar mass of glycine. Glycine has the formula: \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}_{2} \mathrm{N}\), so its molar mass is: \(2 \times 12.01 + 5 \times 1.01 + 2 \times 16.00 + 14.01 = 75.07 g/mol\)
02

Find the number of moles of glycine in 5.00g

We can now use the molar mass of glycine to find the number of moles present in \(5.00g\): Number of moles = \(\frac{5.00 g}{75.07 g/mol} = 0.0666 mol\)
03

Calculate the number of nitrogen atoms in 0.0666 moles of glycine

Next, we need to find the number of nitrogen atoms per molecule of the substance. Glycine has one nitrogen atom per molecule. Thus, we will multiply the number of moles of glycine by the Avogadro's constant and the number of nitrogen atoms per molecule. Number of nitrogen atoms = \(0.0666 mol \times 6.022 \times 10^{23} atoms/mol = 4.01 \times 10^{22} N\ atoms \) b. Magnesium nitride
04

Calculate the molar mass of magnesium nitride

First, we need to determine the molar mass of magnesium nitride: Magnesium nitride has the formula: \(\mathrm{Mg}_{3} \mathrm{N}_{2}\), so its molar mass is: \(3 \times 24.31 + 2 \times 14.01 = 100.95 g/mol\)
05

Find the number of moles of magnesium nitride in 5.00g

We can now use the molar mass of magnesium nitride to find the number of moles present in \(5.00g\): Number of moles = \(\frac{5.00 g}{100.95 g/mol} = 0.0495 mol\)
06

Calculate the number of nitrogen atoms in 0.0495 moles of magnesium nitride

Magnesium nitride has two nitrogen atoms per molecule. So, we will multiply the number of moles of magnesium nitride by the Avogadro's constant and the number of nitrogen atoms per molecule. Number of nitrogen atoms = \(0.0495 mol \times 6.022 \times 10^{23} atoms/mol \times 2 = 5.96 \times 10^{22} N\ atoms\) c&d. Complete using the same steps as in a. and b.

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Most popular questions from this chapter

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