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Calculate the number of moles and the mass of the solute in each of the followin...
Mar 14, 2024
Calculate the number of moles and the mass of the solute in each of the following solutions: (a) 2.00 L2.00 \mathrm{~L} of 18.5MH2SO418.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}, concentrated sulfuric acid (b) 100.0 mL100.0 \mathrm{~mL} of 3.8×10−5MNaCN3.8 \times 10^{-5} \mathrm{M} \mathrm{NaCN}, the minimum lethal concentration of sodium cyanide in blood serum (c) 5.50 L5.50 \mathrm{~L} of 13.3MH2CO13.3 \mathrm{M} \quad \mathrm{H}_{2} \mathrm{CO}, the formaldehyde used to "fix" tissue samples (d) 325 mL325 \mathrm{~mL} of 1.8×10−6MFeSO41.8 \times 10^{-6} \mathrm{M} \mathrm{FeSO}_{4}, the minimum concentration of iron sulfate detectable by taste in drinking water
Solution by Steps
step 1
Calculate the number of moles of H2SO4\mathrm{H}_{2} \mathrm{SO}_{4} using the formula: number of moles = volume in liters ×\times molarity (M)
step 2
Number of moles = 2.00 L×18.5 M2.00 \mathrm{~L} \times 18.5 \mathrm{~M}
step 3
Number of moles = 37.0037.00 moles
step 4
Calculate the mass of the solute using the formula: mass of solute = (number of moles) ×\times molar mass of H2SO4\mathrm{H}_{2} \mathrm{SO}_{4}
step 5
Molar mass of H2SO4\mathrm{H}_{2} \mathrm{SO}_{4} is approximately 98.079 g/mol98.079 \mathrm{~g/mol}
step 6
Mass of solute = 37.00 moles×98.079 g/mol37.00 \mathrm{~moles} \times 98.079 \mathrm{~g/mol}
step 7
Mass of solute = 3628.93 g3628.93 \mathrm{~g}
Answer
Number of moles: 37.0037.00 moles, Mass of solute: 3628.93 g3628.93 \mathrm{~g}
Key Concept
Calculating moles and mass of a solute
Explanation
The number of moles is found by multiplying volume by molarity. The mass is then found by multiplying the number of moles by the molar mass of the solute.
(b) For 100.0 mL100.0 \mathrm{~mL} of 3.8×10−5MNaCN3.8 \times 10^{-5} \mathrm{M} \mathrm{NaCN}
step 1
Convert volume from milliliters to liters: 100.0 mL=0.1000 L100.0 \mathrm{~mL} = 0.1000 \mathrm{~L}
step 2
Calculate the number of moles of NaCN\mathrm{NaCN} using the formula: number of moles = volume in liters ×\times molarity (M)
step 3
Number of moles = 0.1000 L×3.8×10−5 M0.1000 \mathrm{~L} \times 3.8 \times 10^{-5} \mathrm{~M}
step 4
Number of moles = 3.8×10−63.8 \times 10^{-6} moles
step 5
Calculate the mass of the solute using the formula: mass of solute = (number of moles) ×\times molar mass of NaCN\mathrm{NaCN}
step 6
Molar mass of NaCN\mathrm{NaCN} is approximately 49.01 g/mol49.01 \mathrm{~g/mol}
step 7
Mass of solute = 3.8×10−6 moles×49.01 g/mol3.8 \times 10^{-6} \mathrm{~moles} \times 49.01 \mathrm{~g/mol}
step 8
Mass of solute = 0.186238 g0.186238 \mathrm{~g}
Answer
Number of moles: 3.8×10−63.8 \times 10^{-6} moles, Mass of solute: 0.186238 g0.186238 \mathrm{~g}
Key Concept
Calculating moles and mass of a solute
Explanation
The number of moles is found by multiplying volume by molarity. The mass is then found by multiplying the number of moles by the molar mass of the solute.
(c) For 5.50 L5.50 \mathrm{~L} of 13.3MH2CO13.3 \mathrm{M} \quad \mathrm{H}_{2} \mathrm{CO}
step 1
Calculate the number of moles of H2CO\mathrm{H}_{2} \mathrm{CO} using the formula: number of moles = volume in liters ×\times molarity (M)
step 2
Number of moles = 5.50 L×13.3 M5.50 \mathrm{~L} \times 13.3 \mathrm{~M}
step 3
Number of moles = 73.1573.15 moles
step 4
Calculate the mass of the solute using the formula: mass of solute = (number of moles) ×\times molar mass of H2CO\mathrm{H}_{2} \mathrm{CO}
step 5
Molar mass of H2CO\mathrm{H}_{2} \mathrm{CO} is approximately 30.031 g/mol30.031 \mathrm{~g/mol}
step 6
Mass of solute = 73.15 moles×30.031 g/mol73.15 \mathrm{~moles} \times 30.031 \mathrm{~g/mol}
step 7
Mass of solute = 2196.77 g2196.77 \mathrm{~g}
Answer
Number of moles: 73.1573.15 moles, Mass of solute: 2196.77 g2196.77 \mathrm{~g}
Key Concept
Calculating moles and mass of a solute
Explanation
The number of moles is found by multiplying volume by molarity. The mass is then found by multiplying the number of moles by the molar mass of the solute.
(d) For 325 mL325 \mathrm{~mL} of 1.8×10−6MFeSO41.8 \times 10^{-6} \mathrm{M} \mathrm{FeSO}_{4}
step 1
Convert volume from milliliters to liters: 325 mL=0.325 L325 \mathrm{~mL} = 0.325 \mathrm{~L}
step 2
Calculate the number of moles of FeSO4\mathrm{FeSO}_{4} using the formula: number of moles = volume in liters ×\times molarity (M)
step 3
Number of moles = 0.325 L×1.8×10−6 M0.325 \mathrm{~L} \times 1.8 \times 10^{-6} \mathrm{~M}
step 4
Number of moles = 5.85×10−75.85 \times 10^{-7} moles
step 5
Calculate the mass of the solute using the formula: mass of solute = (number of moles) ×\times molar mass of FeSO4\mathrm{FeSO}_{4}
step 6
Molar mass of FeSO4\mathrm{FeSO}_{4} is approximately 151.91 g/mol151.91 \mathrm{~g/mol}
step 7
Mass of solute = 5.85×10−7 moles×151.91 g/mol5.85 \times 10^{-7} \mathrm{~moles} \times 151.91 \mathrm{~g/mol}
step 8
Mass of solute = 0.08886835 g0.08886835 \mathrm{~g}
Answer
Number of moles: 5.85×10−75.85 \times 10^{-7} moles, Mass of solute: 0.08886835 g0.08886835 \mathrm{~g}
Key Concept
Calculating moles and mass of a solute
Explanation
The number of moles is found by multiplying volume by molarity. The mass is then found by multiplying the number of moles by the molar mass of the solute.
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