mass fractions of dysprosium hydride

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dysprosium hydride | elemental composition

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$Find the elemental composition for dysprosium hydride 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: DyH_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 Dy (dysprosium) | 1 H (hydrogen) | 3 N_atoms = 1 + 3 = 4 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 Dy (dysprosium) | 1 | 1/4 H (hydrogen) | 3 | 3/4 Check: 1/4 + 3/4 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Dy (dysprosium) | 1 | 1/4 × 100% = 25.0% H (hydrogen) | 3 | 3/4 × 100% = 75.0% 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 Dy (dysprosium) | 1 | 25.0% | 162.500 H (hydrogen) | 3 | 75.0% | 1.008 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 Dy (dysprosium) | 1 | 25.0% | 162.500 | 1 × 162.500 = 162.500 H (hydrogen) | 3 | 75.0% | 1.008 | 3 × 1.008 = 3.024 m = 162.500 u + 3.024 u = 165.524 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 Dy (dysprosium) | 1 | 25.0% | 162.500/165.524 H (hydrogen) | 3 | 75.0% | 3.024/165.524 Check: 162.500/165.524 + 3.024/165.524 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Dy (dysprosium) | 1 | 25.0% | 162.500/165.524 × 100% = 98.17% H (hydrogen) | 3 | 75.0% | 3.024/165.524 × 100% = 1.827%$

Find the elemental composition for dysprosium hydride 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: DyH_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 Dy (dysprosium) | 1 H (hydrogen) | 3 N_atoms = 1 + 3 = 4 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 Dy (dysprosium) | 1 | 1/4 H (hydrogen) | 3 | 3/4 Check: 1/4 + 3/4 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Dy (dysprosium) | 1 | 1/4 × 100% = 25.0% H (hydrogen) | 3 | 3/4 × 100% = 75.0% 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 Dy (dysprosium) | 1 | 25.0% | 162.500 H (hydrogen) | 3 | 75.0% | 1.008 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 Dy (dysprosium) | 1 | 25.0% | 162.500 | 1 × 162.500 = 162.500 H (hydrogen) | 3 | 75.0% | 1.008 | 3 × 1.008 = 3.024 m = 162.500 u + 3.024 u = 165.524 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 Dy (dysprosium) | 1 | 25.0% | 162.500/165.524 H (hydrogen) | 3 | 75.0% | 3.024/165.524 Check: 162.500/165.524 + 3.024/165.524 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Dy (dysprosium) | 1 | 25.0% | 162.500/165.524 × 100% = 98.17% H (hydrogen) | 3 | 75.0% | 3.024/165.524 × 100% = 1.827%