Input interpretation
![lithium zirconate | elemental composition](../image_source/f556633e35a23deb2bf28118d733c6a8.png)
lithium zirconate | elemental composition
Result
![Find the elemental composition for lithium zirconate in terms of the atom and mass percents: atom percent = N_i/N_atoms × 100% mass percent = (N_im_i)/m × 100% Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i, m_i, N_atoms and m using these items. • Finally, compute the percents and check the results. Write the chemical formula: Li_2ZrO_3 Use the chemical formula to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms, per molecule: | number of atoms Li (lithium) | 2 O (oxygen) | 3 Zr (zirconium) | 1 N_atoms = 2 + 3 + 1 = 6 Divide each N_i by N_atoms to calculate atom fractions. Then use the property that atom fractions must sum to one to check the work: | number of atoms | atom fraction Li (lithium) | 2 | 2/6 O (oxygen) | 3 | 3/6 Zr (zirconium) | 1 | 1/6 Check: 2/6 + 3/6 + 1/6 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Li (lithium) | 2 | 2/6 × 100% = 33.3% O (oxygen) | 3 | 3/6 × 100% = 50.0% Zr (zirconium) | 1 | 1/6 × 100% = 16.7% Look up the atomic mass, m_i, in unified atomic mass units, u, for each element in the periodic table: | number of atoms | atom percent | atomic mass/u Li (lithium) | 2 | 33.3% | 6.94 O (oxygen) | 3 | 50.0% | 15.999 Zr (zirconium) | 1 | 16.7% | 91.224 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molecular mass, m: | number of atoms | atom percent | atomic mass/u | mass/u Li (lithium) | 2 | 33.3% | 6.94 | 2 × 6.94 = 13.88 O (oxygen) | 3 | 50.0% | 15.999 | 3 × 15.999 = 47.997 Zr (zirconium) | 1 | 16.7% | 91.224 | 1 × 91.224 = 91.224 m = 13.88 u + 47.997 u + 91.224 u = 153.101 u Divide the mass for each element by m to calculate mass fractions. Then use the property that mass fractions must sum to one to check the work: | number of atoms | atom percent | mass fraction Li (lithium) | 2 | 33.3% | 13.88/153.101 O (oxygen) | 3 | 50.0% | 47.997/153.101 Zr (zirconium) | 1 | 16.7% | 91.224/153.101 Check: 13.88/153.101 + 47.997/153.101 + 91.224/153.101 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Li (lithium) | 2 | 33.3% | 13.88/153.101 × 100% = 9.07% O (oxygen) | 3 | 50.0% | 47.997/153.101 × 100% = 31.35% Zr (zirconium) | 1 | 16.7% | 91.224/153.101 × 100% = 59.58%](../image_source/c722dd236708a455e4722f681d1f7d9c.png)
Find the elemental composition for lithium zirconate in terms of the atom and mass percents: atom percent = N_i/N_atoms × 100% mass percent = (N_im_i)/m × 100% Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i, m_i, N_atoms and m using these items. • Finally, compute the percents and check the results. Write the chemical formula: Li_2ZrO_3 Use the chemical formula to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms, per molecule: | number of atoms Li (lithium) | 2 O (oxygen) | 3 Zr (zirconium) | 1 N_atoms = 2 + 3 + 1 = 6 Divide each N_i by N_atoms to calculate atom fractions. Then use the property that atom fractions must sum to one to check the work: | number of atoms | atom fraction Li (lithium) | 2 | 2/6 O (oxygen) | 3 | 3/6 Zr (zirconium) | 1 | 1/6 Check: 2/6 + 3/6 + 1/6 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Li (lithium) | 2 | 2/6 × 100% = 33.3% O (oxygen) | 3 | 3/6 × 100% = 50.0% Zr (zirconium) | 1 | 1/6 × 100% = 16.7% Look up the atomic mass, m_i, in unified atomic mass units, u, for each element in the periodic table: | number of atoms | atom percent | atomic mass/u Li (lithium) | 2 | 33.3% | 6.94 O (oxygen) | 3 | 50.0% | 15.999 Zr (zirconium) | 1 | 16.7% | 91.224 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molecular mass, m: | number of atoms | atom percent | atomic mass/u | mass/u Li (lithium) | 2 | 33.3% | 6.94 | 2 × 6.94 = 13.88 O (oxygen) | 3 | 50.0% | 15.999 | 3 × 15.999 = 47.997 Zr (zirconium) | 1 | 16.7% | 91.224 | 1 × 91.224 = 91.224 m = 13.88 u + 47.997 u + 91.224 u = 153.101 u Divide the mass for each element by m to calculate mass fractions. Then use the property that mass fractions must sum to one to check the work: | number of atoms | atom percent | mass fraction Li (lithium) | 2 | 33.3% | 13.88/153.101 O (oxygen) | 3 | 50.0% | 47.997/153.101 Zr (zirconium) | 1 | 16.7% | 91.224/153.101 Check: 13.88/153.101 + 47.997/153.101 + 91.224/153.101 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Li (lithium) | 2 | 33.3% | 13.88/153.101 × 100% = 9.07% O (oxygen) | 3 | 50.0% | 47.997/153.101 × 100% = 31.35% Zr (zirconium) | 1 | 16.7% | 91.224/153.101 × 100% = 59.58%
Mass fraction pie chart
![Mass fraction pie chart](../image_source/84f43fbef76218f1af5d2d8b9b7ca522.png)
Mass fraction pie chart