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Answers to More Chapter 11 Study Questions

  1. 5.00 g \(\ce{NaClO}\) per 100. g solution; contains 95.0 g \(\ce{H2O}\).

\(\mathrm{5.00\:g\:NaClO\times\dfrac{1\:mole\:NaClO}{74.5\:g\:NaClO}=0.0671\:mol}\); \(\mathrm{95.0\:g\:H_2O\times\dfrac{1\:kg\:H_2O}{1000\:g\:H_2O}=0.0950\:kg\:H_2O}\)

\(\mathrm{molality=\dfrac{moles\:NaClO}{kg\:H_2O}=\dfrac{0.0671\:moles\:NaClO}{0.0950\:kg\:H_2O}=0.706\: m}\)

\(\mathrm{95.0\:g\:H_2O\times\dfrac{1\:mole\:H_2O}{18.0\:g\:H_2O}=5.28\:moles\:H_2O}\);  \(\mathrm{total\: moles =  5.28 + 0.07 = 5.35\: moles}\)

\(\mathrm{mole\:fraction=\dfrac{moles\:NaClO}{total\:moles}=\dfrac{0.0671\:moles\:NaClO}{5.35\:moles}=0.0125}\)

 

  1. \(\mathrm{12.8\:g\:NaOH\times\dfrac{100\:g\:solution}{32.0\:g\:NaOH}=40.0\:g\:solution}\)

 

  1. 0.0476 moles \(\ce{NaOH}\); \(\mathrm{(1-0.0476) = 0.952\: mole\: H_2O}\).

\(\mathrm{0.0476\:mol\:NaOH\times\dfrac{40.0\:g\:NaOH}{1\:mol\:NaOH}=1.90\:g\:NaOH}\)

\(\mathrm{0.952\:mol\:H_2O\times\dfrac{18.0\:g\:H_2O}{1\:mol\:H_2O}=17.1\:g\:H_2O}\);  \(\mathrm{\textrm{mass of solution} =  17.1 + 1.90 = 19.0\: g\: solution}\)

\(\mathrm{mass\:percent=\dfrac{mass\:NaOH}{mass\:solution}\times100\%=\dfrac{1.90\:g\:NaOH}{19.0\:g\:solution}=10.0\%\:NaOH}\)

\(\mathrm{\dfrac{0.0476\:mol\:NaOH}{19.0\:g\:solution}\times\dfrac{1.11\:g}{1\:mL}\times\dfrac{1000\:mL}{1\:L}=2.78\:M\:NaOH}\)

 

  1. A saturated solution at 80.°C contains 167 g \(\ce{KNO3}\) dissolved in 100. g \(\ce{H2O}\).

\(\mathrm{167\:g\:KNO_3\times\dfrac{1\:mol\:KNO_3}{101.1\:g\:KNO_3}=1.65\:mol\:KNO_3}\)

\(\mathrm{100.\:g\:H_2O\times\dfrac{1\:mol\:H_2O}{18.0\:g\:H_2O}=5.56\:mol\:H_2O}\);  \(\mathrm{total\: moles = 1.65 + 5.56 = 7.21\: moles}\)

\(\mathrm{mole\:fraction=\dfrac{moles\:KNO_3}{total\:moles}=\dfrac{1.65\:moles\:KNO_3}{7.21\:moles}=0.229}\)

 

  1. 44.6 g \(\ce{C7H8}\) in 250. g of benzene.

From the chart, \(\mathrm{bp(benzene) = 80.10^\circ C}\);  \(\mathrm{kb(benzene) = 2.53\, ^\circ C\cdot kg/mol}\)

\(\mathrm{\Delta T_b=k_b\times\dfrac{mol\:solute\:particles}{kg\:solvent}}\)

\(\mathrm{44.6\:C_7H_8\times\dfrac{1\:mol\:C_7H_8}{92.0\:g\:C_7H_8}=0.485\:moles\:C_7H_8}\)

\(\mathrm{250.\:g\:benzene\times\dfrac{1\:kg\:benzene}{1000\:g\:benzene}=0.250\:kg\:benzene}\)

\(\mathrm{\Delta T_b=2.53\:^\circ C\times\dfrac{0.485\:moles}{0.250\:kg\:benzene}=4.91\:^\circ C}\);   \(\mathrm{T_b = 80.10 + 4.91 = 85.01^\circ C}\)

 

  1. \(\mathrm{\Delta T_F=k_F\times\dfrac{mol\:solute\:particles}{kg\:solvent}}\);  \(\mathrm{k_F(H_2O) = 1.86\, ^\circ C\cdot kg/mol}\); \(\mathrm{\Delta T_f = 10.0^\circ C}\)

\(\mathrm{\Delta T_F=1.86\times\dfrac{moles\:solute\:particles}{kg\:H_2O}}\); \(\mathrm{10.0\:^\circ C=1.86\times\dfrac{moles\:solute\:particles}{0.200\:kg\:H_2O}}\)

\(\mathrm{moles=\dfrac{10.0}{1.86}\times0.200\:kg=1.08\:mol\:particles}\)

\(\mathrm{1.08\:mol\:particles\times\dfrac{1\:mol\:CaCl_2}{3\:mol\:particles}\times\dfrac{111\:g\:CaCl_2}{1\:mol\:CaCl_2}=40.0\:g\:CaCl_2}\)

 

  1. 9.00 g solute; 300.0 g water; \(\mathrm{T_f = -0.930^\circ C}\).  \(\mathrm{\Delta T_F=k_F\times\dfrac{mol\:solute\:particles}{kg\:solvent}}\)

\(\mathrm{300.\: g\: H_2O = 0.300\: kg\: H_2O}\).  \(\mathrm{\Delta T_f = 0.930^\circ C}\);  \(\mathrm{k_F(H_2O) = 1.86\, ^\circ C\cdot kg/mol}\)

\(\mathrm{0.930\,^\circ C=1.86\,\dfrac{^\circ C\cdot kg}{mol}\times\dfrac{mol\:solute}{0.300\:kg\:H_2O}}\);  \(\mathrm{moles=\dfrac{0.930}{1.86}\times0.300=0.150\:moles}\)

\(\mathrm{molar\:mass=\dfrac{mass}{moles}=\dfrac{9.00\:g}{0.150\:mol}=60.0\:g/mol}\);  alcohol is propanol:  \(\ce{C3H8O}\)