element mass fraction of hafnium(II) hydride

Input interpretation

Image
Text

hafnium(II) hydride | elemental composition

Result

Image
Text

$Find the elemental composition for hafnium(II) 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: HfH_2 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 H (hydrogen) | 2 Hf (hafnium) | 1 N_atoms = 2 + 1 = 3 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 H (hydrogen) | 2 | 2/3 Hf (hafnium) | 1 | 1/3 Check: 2/3 + 1/3 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 2 | 2/3 × 100% = 66.7% Hf (hafnium) | 1 | 1/3 × 100% = 33.3% 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 H (hydrogen) | 2 | 66.7% | 1.008 Hf (hafnium) | 1 | 33.3% | 178.49 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 H (hydrogen) | 2 | 66.7% | 1.008 | 2 × 1.008 = 2.016 Hf (hafnium) | 1 | 33.3% | 178.49 | 1 × 178.49 = 178.49 m = 2.016 u + 178.49 u = 180.506 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 H (hydrogen) | 2 | 66.7% | 2.016/180.506 Hf (hafnium) | 1 | 33.3% | 178.49/180.506 Check: 2.016/180.506 + 178.49/180.506 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 2 | 66.7% | 2.016/180.506 × 100% = 1.117% Hf (hafnium) | 1 | 33.3% | 178.49/180.506 × 100% = 98.88%$

Find the elemental composition for hafnium(II) 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: HfH_2 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 H (hydrogen) | 2 Hf (hafnium) | 1 N_atoms = 2 + 1 = 3 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 H (hydrogen) | 2 | 2/3 Hf (hafnium) | 1 | 1/3 Check: 2/3 + 1/3 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 2 | 2/3 × 100% = 66.7% Hf (hafnium) | 1 | 1/3 × 100% = 33.3% 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 H (hydrogen) | 2 | 66.7% | 1.008 Hf (hafnium) | 1 | 33.3% | 178.49 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 H (hydrogen) | 2 | 66.7% | 1.008 | 2 × 1.008 = 2.016 Hf (hafnium) | 1 | 33.3% | 178.49 | 1 × 178.49 = 178.49 m = 2.016 u + 178.49 u = 180.506 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 H (hydrogen) | 2 | 66.7% | 2.016/180.506 Hf (hafnium) | 1 | 33.3% | 178.49/180.506 Check: 2.016/180.506 + 178.49/180.506 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 2 | 66.7% | 2.016/180.506 × 100% = 1.117% Hf (hafnium) | 1 | 33.3% | 178.49/180.506 × 100% = 98.88%