mass fractions of chromium boride

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chromium boride | elemental composition

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$Find the elemental composition for chromium boride 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: CrB Use the chemical formula, CrB, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms B (boron) | 1 Cr (chromium) | 1 N_atoms = 1 + 1 = 2 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 B (boron) | 1 | 1/2 Cr (chromium) | 1 | 1/2 Check: 1/2 + 1/2 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent B (boron) | 1 | 1/2 × 100% = 50.0% Cr (chromium) | 1 | 1/2 × 100% = 50.0% 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 B (boron) | 1 | 50.0% | 10.81 Cr (chromium) | 1 | 50.0% | 51.9961 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 B (boron) | 1 | 50.0% | 10.81 | 1 × 10.81 = 10.81 Cr (chromium) | 1 | 50.0% | 51.9961 | 1 × 51.9961 = 51.9961 m = 10.81 u + 51.9961 u = 62.8061 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 B (boron) | 1 | 50.0% | 10.81/62.8061 Cr (chromium) | 1 | 50.0% | 51.9961/62.8061 Check: 10.81/62.8061 + 51.9961/62.8061 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent B (boron) | 1 | 50.0% | 10.81/62.8061 × 100% = 17.21% Cr (chromium) | 1 | 50.0% | 51.9961/62.8061 × 100% = 82.79%$

Find the elemental composition for chromium boride 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: CrB Use the chemical formula, CrB, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms B (boron) | 1 Cr (chromium) | 1 N_atoms = 1 + 1 = 2 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 B (boron) | 1 | 1/2 Cr (chromium) | 1 | 1/2 Check: 1/2 + 1/2 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent B (boron) | 1 | 1/2 × 100% = 50.0% Cr (chromium) | 1 | 1/2 × 100% = 50.0% 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 B (boron) | 1 | 50.0% | 10.81 Cr (chromium) | 1 | 50.0% | 51.9961 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 B (boron) | 1 | 50.0% | 10.81 | 1 × 10.81 = 10.81 Cr (chromium) | 1 | 50.0% | 51.9961 | 1 × 51.9961 = 51.9961 m = 10.81 u + 51.9961 u = 62.8061 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 B (boron) | 1 | 50.0% | 10.81/62.8061 Cr (chromium) | 1 | 50.0% | 51.9961/62.8061 Check: 10.81/62.8061 + 51.9961/62.8061 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent B (boron) | 1 | 50.0% | 10.81/62.8061 × 100% = 17.21% Cr (chromium) | 1 | 50.0% | 51.9961/62.8061 × 100% = 82.79%