mass fractions of cesium orthovanadate

cesium orthovanadate | elemental composition

Find the elemental composition for cesium orthovanadate 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: Cs_3VO_4 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 Cs (cesium) | 3 O (oxygen) | 4 V (vanadium) | 1 N_atoms = 3 + 4 + 1 = 8 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 Cs (cesium) | 3 | 3/8 O (oxygen) | 4 | 4/8 V (vanadium) | 1 | 1/8 Check: 3/8 + 4/8 + 1/8 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cs (cesium) | 3 | 3/8 × 100% = 37.5% O (oxygen) | 4 | 4/8 × 100% = 50.0% V (vanadium) | 1 | 1/8 × 100% = 12.5% 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 Cs (cesium) | 3 | 37.5% | 132.90545196 O (oxygen) | 4 | 50.0% | 15.999 V (vanadium) | 1 | 12.5% | 50.9415 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 Cs (cesium) | 3 | 37.5% | 132.90545196 | 3 × 132.90545196 = 398.71635588 O (oxygen) | 4 | 50.0% | 15.999 | 4 × 15.999 = 63.996 V (vanadium) | 1 | 12.5% | 50.9415 | 1 × 50.9415 = 50.9415 m = 398.71635588 u + 63.996 u + 50.9415 u = 513.65385588 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 Cs (cesium) | 3 | 37.5% | 398.71635588/513.65385588 O (oxygen) | 4 | 50.0% | 63.996/513.65385588 V (vanadium) | 1 | 12.5% | 50.9415/513.65385588 Check: 398.71635588/513.65385588 + 63.996/513.65385588 + 50.9415/513.65385588 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cs (cesium) | 3 | 37.5% | 398.71635588/513.65385588 × 100% = 77.62% O (oxygen) | 4 | 50.0% | 63.996/513.65385588 × 100% = 12.46% V (vanadium) | 1 | 12.5% | 50.9415/513.65385588 × 100% = 9.917%

Mass fraction pie chart