Input interpretation
![gadolinium(III) bromide hydrate | molar mass](../image_source/66a2c09b5289ea7c5716c7bb4eb9998a.png)
gadolinium(III) bromide hydrate | molar mass
Result
![Find the molar mass, M, for gadolinium(III) bromide hydrate: M = sum _iN_im_i Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i and m_i using these items. • Finally, compute the mass. Write the chemical formula: GdBr_3·xH_2O Use the chemical formula to count the number of atoms, N_i, for each element: | N_i Br (bromine) | 3 Gd (gadolinium) | 1 H (hydrogen) | 2 O (oxygen) | 1 Look up the atomic mass, m_i, in g·mol^(-1) for each element in the periodic table: | N_i | m_i/g·mol^(-1) Br (bromine) | 3 | 79.904 Gd (gadolinium) | 1 | 157.25 H (hydrogen) | 2 | 1.008 O (oxygen) | 1 | 15.999 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molar mass, M: Answer: | | | N_i | m_i/g·mol^(-1) | mass/g·mol^(-1) Br (bromine) | 3 | 79.904 | 3 × 79.904 = 239.712 Gd (gadolinium) | 1 | 157.25 | 1 × 157.25 = 157.25 H (hydrogen) | 2 | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 1 | 15.999 | 1 × 15.999 = 15.999 M = 239.712 g/mol + 157.25 g/mol + 2.016 g/mol + 15.999 g/mol = 414.98 g/mol](../image_source/05f5f8a597c1061910e7f76e9dd9b201.png)
Find the molar mass, M, for gadolinium(III) bromide hydrate: M = sum _iN_im_i Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i and m_i using these items. • Finally, compute the mass. Write the chemical formula: GdBr_3·xH_2O Use the chemical formula to count the number of atoms, N_i, for each element: | N_i Br (bromine) | 3 Gd (gadolinium) | 1 H (hydrogen) | 2 O (oxygen) | 1 Look up the atomic mass, m_i, in g·mol^(-1) for each element in the periodic table: | N_i | m_i/g·mol^(-1) Br (bromine) | 3 | 79.904 Gd (gadolinium) | 1 | 157.25 H (hydrogen) | 2 | 1.008 O (oxygen) | 1 | 15.999 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molar mass, M: Answer: | | | N_i | m_i/g·mol^(-1) | mass/g·mol^(-1) Br (bromine) | 3 | 79.904 | 3 × 79.904 = 239.712 Gd (gadolinium) | 1 | 157.25 | 1 × 157.25 = 157.25 H (hydrogen) | 2 | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 1 | 15.999 | 1 × 15.999 = 15.999 M = 239.712 g/mol + 157.25 g/mol + 2.016 g/mol + 15.999 g/mol = 414.98 g/mol
Unit conversion
![0.41498 kg/mol (kilograms per mole)](../image_source/015e681ffc15d83265f839512248214a.png)
0.41498 kg/mol (kilograms per mole)
Comparisons
![≈ 0.58 × molar mass of fullerene ( ≈ 721 g/mol )](../image_source/0e7a5d65cb2dd5e1d73e5ceb36e514cd.png)
≈ 0.58 × molar mass of fullerene ( ≈ 721 g/mol )
![≈ 2.1 × molar mass of caffeine ( ≈ 194 g/mol )](../image_source/f6e928e05d405ba817e538b856e8a5a8.png)
≈ 2.1 × molar mass of caffeine ( ≈ 194 g/mol )
![≈ 7.1 × molar mass of sodium chloride ( ≈ 58 g/mol )](../image_source/493fdee3cfc9257ea6800cdb0551e19c.png)
≈ 7.1 × molar mass of sodium chloride ( ≈ 58 g/mol )
Corresponding quantities
![Mass of a molecule m from m = M/N_A: | 6.9×10^-22 grams | 6.9×10^-25 kg (kilograms) | 415 u (unified atomic mass units) | 415 Da (daltons)](../image_source/31ea1472e7d47ed6557534690b61a7e0.png)
Mass of a molecule m from m = M/N_A: | 6.9×10^-22 grams | 6.9×10^-25 kg (kilograms) | 415 u (unified atomic mass units) | 415 Da (daltons)
![Relative molecular mass M_r from M_r = M_u/M: | 415](../image_source/19aa4b3f9e942ef210c96ee2b8908208.png)
Relative molecular mass M_r from M_r = M_u/M: | 415