mass fractions of zirconium-nickel alloy (30:70)

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zirconium-nickel alloy (30:70) | elemental composition

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$Find the elemental composition for zirconium-nickel alloy (30:70) 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: NiZr 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 Ni (nickel) | 1 Zr (zirconium) | 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 Ni (nickel) | 1 | 1/2 Zr (zirconium) | 1 | 1/2 Check: 1/2 + 1/2 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Ni (nickel) | 1 | 1/2 × 100% = 50.0% Zr (zirconium) | 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 Ni (nickel) | 1 | 50.0% | 58.6934 Zr (zirconium) | 1 | 50.0% | 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 Ni (nickel) | 1 | 50.0% | 58.6934 | 1 × 58.6934 = 58.6934 Zr (zirconium) | 1 | 50.0% | 91.224 | 1 × 91.224 = 91.224 m = 58.6934 u + 91.224 u = 149.9174 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 Ni (nickel) | 1 | 50.0% | 58.6934/149.9174 Zr (zirconium) | 1 | 50.0% | 91.224/149.9174 Check: 58.6934/149.9174 + 91.224/149.9174 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Ni (nickel) | 1 | 50.0% | 58.6934/149.9174 × 100% = 39.15% Zr (zirconium) | 1 | 50.0% | 91.224/149.9174 × 100% = 60.85%$

Find the elemental composition for zirconium-nickel alloy (30:70) 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: NiZr 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 Ni (nickel) | 1 Zr (zirconium) | 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 Ni (nickel) | 1 | 1/2 Zr (zirconium) | 1 | 1/2 Check: 1/2 + 1/2 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Ni (nickel) | 1 | 1/2 × 100% = 50.0% Zr (zirconium) | 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 Ni (nickel) | 1 | 50.0% | 58.6934 Zr (zirconium) | 1 | 50.0% | 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 Ni (nickel) | 1 | 50.0% | 58.6934 | 1 × 58.6934 = 58.6934 Zr (zirconium) | 1 | 50.0% | 91.224 | 1 × 91.224 = 91.224 m = 58.6934 u + 91.224 u = 149.9174 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 Ni (nickel) | 1 | 50.0% | 58.6934/149.9174 Zr (zirconium) | 1 | 50.0% | 91.224/149.9174 Check: 58.6934/149.9174 + 91.224/149.9174 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Ni (nickel) | 1 | 50.0% | 58.6934/149.9174 × 100% = 39.15% Zr (zirconium) | 1 | 50.0% | 91.224/149.9174 × 100% = 60.85%