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Answer the following questions a) How many atoms are in 0.5 moles of Sodium (Na)?(1) b) How many atoms are in 0.45 grams of Iron?(1) c) How many molecules are in 0.75 moles of H2O?(1) d) CH4 has 3.01 x 1023 molecules, Calculate its number of moles.(2)

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Here are the solutions to questions 5, 6, 7, 8, and 9.

Question 5:
Given: Mass of Magnesium (Mg) = 24 grams.
Atomic mass of Mg = 24.305 g/mol. (Using a more precise value for calculations)

a) Calculate the number of moles of magnesium present.

  1. Use the formula for moles.

    Moles=MassMolar mass\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}}

  2. Substitute the given values.

    Moles of Mg=24 g24.305 g/mol\text{Moles of Mg} = \frac{24 \text{ g}}{24.305 \text{ g/mol}} Moles of Mg≈0.987 mol\text{Moles of Mg} \approx 0.987 \text{ mol}

    The number of moles of magnesium present is 0.987 mol\boxed{\text{0.987 mol}}.

    b) Determine the number of atoms in the sample.

  3. Use Avogadro's number (6.022×10236.022 \times 10^{23} atoms/mol).

    Number of atoms=Moles×Avogadro’s number\text{Number of atoms} = \text{Moles} \times \text{Avogadro's number}

  4. Substitute the calculated moles.

    Number of atoms of Mg=0.987 mol×(6.022×1023 atoms/mol)\text{Number of atoms of Mg} = 0.987 \text{ mol} \times (6.022 \times 10^{23} \text{ atoms/mol}) Number of atoms of Mg≈5.944×1023 atoms\text{Number of atoms of Mg} \approx 5.944 \times 10^{23} \text{ atoms}

    The number of atoms in the sample is 5.944×1023 atoms\boxed{5.944 \times 10^{23} \text{ atoms}}.

    Question 6:
    Given: Mass of Sodium chloride (NaCl) = 58.5 grams.
    Atomic mass of Na = 22.99 g/mol.
    Atomic mass of Cl = 35.45 g/mol.

    a) Calculate the molar mass of Sodium chloride.

  5. Sum the atomic masses of Na and Cl.

    Molar mass of NaCl=Atomic mass of Na+Atomic mass of Cl\text{Molar mass of NaCl} = \text{Atomic mass of Na} + \text{Atomic mass of Cl} Molar mass of NaCl=22.99 g/mol+35.45 g/mol\text{Molar mass of NaCl} = 22.99 \text{ g/mol} + 35.45 \text{ g/mol} Molar mass of NaCl=58.44 g/mol\text{Molar mass of NaCl} = 58.44 \text{ g/mol}

    The molar mass of Sodium chloride is 58.44 g/mol\boxed{58.44 \text{ g/mol}}.

    b) Determine the number of moles present.

  6. Use the formula for moles.

    Moles=MassMolar mass\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}}

  7. Substitute the given mass and calculated molar mass.

    Moles of NaCl=58.5 g58.44 g/mol\text{Moles of NaCl} = \frac{58.5 \text{ g}}{58.44 \text{ g/mol}} Moles of NaCl≈1.001 mol\text{Moles of NaCl} \approx 1.001 \text{ mol}

    The number of moles present is 1.001 mol\boxed{1.001 \text{ mol}}.

    c) Calculate the number of ions if the salt completely dissociates in water.

  8. Determine the number of ions per formula unit.

    NaCl dissociates into Na+\text{Na}^+ and Cl−\text{Cl}^-, so there are 2 ions per formula unit.

  9. Calculate the total number of formula units.

    Number of formula units=Moles×Avogadro’s number\text{Number of formula units} = \text{Moles} \times \text{Avogadro's number} Number of formula units of NaCl=1.001 mol×(6.022×1023 formula units/mol)\text{Number of formula units of NaCl} = 1.001 \text{ mol} \times (6.022 \times 10^{23} \text{ formula units/mol}) Number of formula units of NaCl≈6.028×1023 formula units\text{Number of formula units of NaCl} \approx 6.028 \times 10^{23} \text{ formula units}

  10. Calculate the total number of ions.

    Number of ions=Number of formula units×2\text{Number of ions} = \text{Number of formula units} \times 2 Number of ions=(6.028×1023)×2\text{Number of ions} = (6.028 \times 10^{23}) \times 2 Number of ions≈1.206×1024 ions\text{Number of ions} \approx 1.206 \times 10^{24} \text{ ions}

    The number of ions is 1.206×1024 ions\boxed{1.206 \times 10^{24} \text{ ions}}.

    Question 7:
    Given: Mass of Lead nitrate Pb(NO3)2\text{Pb(NO}_3)_2 = 98 grams.
    Atomic mass of Pb = 207.2 g/mol.
    Atomic mass of N = 14.01 g/mol.
    Atomic mass of O = 16.00 g/mol.

    a) Calculate the molar mass of Pb(NO3)2\text{Pb(NO}_3)_2.

  11. Sum the atomic masses of all atoms in the formula.

    Molar mass of Pb(NO3)2=Atomic mass of Pb+2×(Atomic mass of N+3×Atomic mass of O)\text{Molar mass of Pb(NO}_3)_2 = \text{Atomic mass of Pb} + 2 \times (\text{Atomic mass of N} + 3 \times \text{Atomic mass of O}) Molar mass of Pb(NO3)2=207.2 g/mol+2×(14.01 g/mol+3×16.00 g/mol)\text{Molar mass of Pb(NO}_3)_2 = 207.2 \text{ g/mol} + 2 \times (14.01 \text{ g/mol} + 3 \times 16.00 \text{ g/mol}) Molar mass of Pb(NO3)2=207.2 g/mol+2×(14.01 g/mol+48.00 g/mol)\text{Molar mass of Pb(NO}_3)_2 = 207.2 \text{ g/mol} + 2 \times (14.01 \text{ g/mol} + 48.00 \text{ g/mol}) Molar mass of Pb(NO3)2=207.2 g/mol+2×(62.01 g/mol)\text{Molar mass of Pb(NO}_3)_2 = 207.2 \text{ g/mol} + 2 \times (62.01 \text{ g/mol}) Molar mass of Pb(NO3)2=207.2 g/mol+124.02 g/mol\text{Molar mass of Pb(NO}_3)_2 = 207.2 \text{ g/mol} + 124.02 \text{ g/mol} Molar mass of Pb(NO3)2=331.22 g/mol\text{Molar mass of Pb(NO}_3)_2 = 331.22 \text{ g/mol}

    The molar mass of Pb(NO3)2\text{Pb(NO}_3)_2 is 331.22 g/mol\boxed{331.22 \text{ g/mol}}.

    b) Determine the number of moles present.

  12. Use the formula for moles.

    Moles=MassMolar mass\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}}

  13. Substitute the given mass and calculated molar mass.

    Moles of Pb(NO3)2=98 g331.22 g/mol\text{Moles of Pb(NO}_3)_2 = \frac{98 \text{ g}}{331.22 \text{ g/mol}} Moles of Pb(NO3)2≈0.296 mol\text{Moles of Pb(NO}_3)_2 \approx 0.296 \text{ mol}

    The number of moles present is 0.296 mol\boxed{0.296 \text{ mol}}.

    c) Find the number of formula units in the sample.

  14. Use Avogadro's number.

    Number of formula units=Moles×Avogadro’s number\text{Number of formula units} = \text{Moles} \times \text{Avogadro's number}

  15. Substitute the calculated moles.

    Number of formula units of Pb(NO3)2=0.296 mol×(6.022×1023 formula units/mol)\text{Number of formula units of Pb(NO}_3)_2 = 0.296 \text{ mol} \times (6.022 \times 10^{23} \text{ formula units/mol}) Number of formula units of Pb(NO3)2≈1.783×1023 formula units\text{Number of formula units of Pb(NO}_3)_2 \approx 1.783 \times 10^{23} \text{ formula units}

    The number of formula units in the sample is 1.783×1023 formula units\boxed{1.783 \times 10^{23} \text{ formula units}}.

    Question 8:
    Given: Mass of Sulfuric acid (H2SO4\text{H}_2\text{SO}_4) = 49 grams.
    Atomic mass of H = 1.008 g/mol.
    Atomic mass of S = 32.07 g/mol.
    Atomic mass of O = 16.00 g/mol.

    a) Calculate the molar mass of H2SO4\text{H}_2\text{SO}_4.

  16. Sum the atomic masses of all atoms in the formula.

    Molar mass of H2SO4=(2×Atomic mass of H)+Atomic mass of S+(4×Atomic mass of O)\text{Molar mass of H}_2\text{SO}_4 = (2 \times \text{Atomic mass of H}) + \text{Atomic mass of S} + (4 \times \text{Atomic mass of O}) Molar mass of H2SO4=(2×1.008 g/mol)+32.07 g/mol+(4×16.00 g/mol)\text{Molar mass of H}_2\text{SO}_4 = (2 \times 1.008 \text{ g/mol}) + 32.07 \text{ g/mol} + (4 \times 16.00 \text{ g/mol}) Molar mass of H2SO4=2.016 g/mol+32.07 g/mol+64.00 g/mol\text{Molar mass of H}_2\text{SO}_4 = 2.016 \text{ g/mol} + 32.07 \text{ g/mol} + 64.00 \text{ g/mol} Molar mass of H2SO4=98.086 g/mol\text{Molar mass of H}_2\text{SO}_4 = 98.086 \text{ g/mol}

    The molar mass of H2SO4\text{H}_2\text{SO}_4 is 98.086 g/mol\boxed{98.086 \text{ g/mol}}.

    b) Calculate the number of moles present.

  17. Use the formula for moles.

    Moles=MassMolar mass\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}}

  18. Substitute the given mass and calculated molar mass.

    Moles of H2SO4=49 g98.086 g/mol\text{Moles of H}_2\text{SO}_4 = \frac{49 \text{ g}}{98.086 \text{ g/mol}} Moles of H2SO4≈0.4995 mol\text{Moles of H}_2\text{SO}_4 \approx 0.4995 \text{ mol}

    The number of moles present is 0.4995 mol\boxed{0.4995 \text{ mol}}.

    c) Determine the number of molecules in the sample.

  19. Use Avogadro's number.

    Number of molecules=Moles×Avogadro’s number\text{Number of molecules} = \text{Moles} \times \text{Avogadro's number}

  20. Substitute the calculated moles.

    Number of molecules of H2SO4=0.4995 mol×(6.022×1023 molecules/mol)\text{Number of molecules of H}_2\text{SO}_4 = 0.4995 \text{ mol} \times (6.022 \times 10^{23} \text{ molecules/mol}) Number of molecules of H2SO4≈3.008×1023 molecules\text{Number of molecules of H}_2\text{SO}_4 \approx 3.008 \times 10^{23} \text{ molecules}

    The number of molecules in the sample is 3.008×1023 molecules\boxed{3.008 \times 10^{23} \text{ molecules}}.

    Question 9:

    a) How many atoms are in 0.5 moles of Sodium (Na)?

  21. Use Avogadro's number.

    Number of atoms=Moles×Avogadro’s number\text{Number of atoms} = \text{Moles} \times \text{Avogadro's number}

  22. Substitute the given moles.

    Number of atoms of Na=0.5 mol×(6.022×1023 atoms/mol)\text{Number of atoms of Na} = 0.5 \text{ mol} \times (6.022 \times 10^{23} \text{ atoms/mol}) Number of atoms of Na=3.011×1023 atoms\text{Number of atoms of Na} = 3.011 \times 10^{23} \text{ atoms}

    There are 3.011×1023 atoms\boxed{3.011 \times 10^{23} \text{ atoms}} in 0.5 moles of Sodium.

    b) How many atoms are in 0.45 grams of Iron (Fe)?
    Atomic mass of Fe = 55.845 g/mol.

  23. Calculate the number of moles of Fe.

    Moles of Fe=MassMolar mass=0.45 g55.845 g/mol\text{Moles of Fe} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{0.45 \text{ g}}{55.845 \text{ g/mol}} Moles of Fe≈0.008058 mol\text{Moles of Fe} \approx 0.008058 \text{ mol}

  24. Calculate the number of atoms.

    Number of atoms of Fe=0.008058 mol×(6.022×1023 atoms/mol)\text{Number of atoms of Fe} = 0.008058 \text{ mol} \times (6.022 \times 10^{23} \text{ atoms/mol}) Number of atoms of Fe≈4.852×1021 atoms\text{Number of atoms of Fe} \approx 4.852 \times 10^{21} \text{ atoms}

    There are 4.852×1021 atoms\boxed{4.852 \times 10^{21} \text{ atoms}} in 0.45 grams of Iron.

    c) How many molecules are in 0.75 moles of H2O\text{H}_2\text{O}?

  25. Use Avogadro's number.

    Number of molecules=Moles×Avogadro’s number\text{Number of molecules} = \text{Moles} \times \text{Avogadro's number}

  26. Substitute the given moles.

    Number of molecules of H2O=0.75 mol×(6.022×1023 molecules/mol)\text{Number of molecules of H}_2\text{O} = 0.75 \text{ mol} \times (6.022 \times 10^{23} \text{ molecules/mol}) Number of molecules of H2O=4.5165×1023 molecules\text{Number of molecules of H}_2\text{O} = 4.5165 \times 10^{23} \text{ molecules}

    There are 4.5165×1023 molecules\boxed{4.5165 \times 10^{23} \text{ molecules}} in 0.75 moles of H2O\text{H}_2\text{O}.

    d) CH4\text{CH}_4 has 3.01×10233.01 \times 10^{23} molecules. Calculate its number of moles.

  27. Use Avogadro's number to convert molecules to moles.

    Moles=Number of moleculesAvogadro’s number\text{Moles} = \frac{\text{Number of molecules}}{\text{Avogadro's number}}

  28. Substitute the given number of molecules.

    Moles of CH4=3.01×1023 molecules6.022×1023 molecules/mol\text{Moles of CH}_4 = \frac{3.01 \times 10^{23} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}} Moles of CH4≈0.4998 mol\text{Moles of CH}_4 \approx 0.4998 \text{ mol}

    The number of moles of CH4\text{CH}_4 is 0.4998 mol\boxed{0.4998 \text{ mol}}.

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