mass fractions of pentaborane(9)

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pentaborane(9) | elemental composition

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$Find the elemental composition for pentaborane(9) 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: B_5H_9 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 B (boron) | 5 H (hydrogen) | 9 N_atoms = 5 + 9 = 14 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) | 5 | 5/14 H (hydrogen) | 9 | 9/14 Check: 5/14 + 9/14 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent B (boron) | 5 | 5/14 × 100% = 35.7% H (hydrogen) | 9 | 9/14 × 100% = 64.3% 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 B (boron) | 5 | 35.7% | 10.81 H (hydrogen) | 9 | 64.3% | 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 B (boron) | 5 | 35.7% | 10.81 | 5 × 10.81 = 54.05 H (hydrogen) | 9 | 64.3% | 1.008 | 9 × 1.008 = 9.072 m = 54.05 u + 9.072 u = 63.122 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) | 5 | 35.7% | 54.05/63.122 H (hydrogen) | 9 | 64.3% | 9.072/63.122 Check: 54.05/63.122 + 9.072/63.122 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent B (boron) | 5 | 35.7% | 54.05/63.122 × 100% = 85.63% H (hydrogen) | 9 | 64.3% | 9.072/63.122 × 100% = 14.37%$

Find the elemental composition for pentaborane(9) 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: B_5H_9 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 B (boron) | 5 H (hydrogen) | 9 N_atoms = 5 + 9 = 14 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) | 5 | 5/14 H (hydrogen) | 9 | 9/14 Check: 5/14 + 9/14 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent B (boron) | 5 | 5/14 × 100% = 35.7% H (hydrogen) | 9 | 9/14 × 100% = 64.3% 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 B (boron) | 5 | 35.7% | 10.81 H (hydrogen) | 9 | 64.3% | 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 B (boron) | 5 | 35.7% | 10.81 | 5 × 10.81 = 54.05 H (hydrogen) | 9 | 64.3% | 1.008 | 9 × 1.008 = 9.072 m = 54.05 u + 9.072 u = 63.122 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) | 5 | 35.7% | 54.05/63.122 H (hydrogen) | 9 | 64.3% | 9.072/63.122 Check: 54.05/63.122 + 9.072/63.122 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent B (boron) | 5 | 35.7% | 54.05/63.122 × 100% = 85.63% H (hydrogen) | 9 | 64.3% | 9.072/63.122 × 100% = 14.37%