Solutions to Practice Problems

stoichiometry: 

1) When 26.5 grams of Mg are reacted with hydrochloric acid, how many grams of magnesium chloride are produced?

                              Mg  +   2HCl  -->  MgCl₂  +  H₂

[26.5 g Mg][  1 mol Mg][1 mol MgCl₂][95.3 g MgCl₂ ]  =  104 g MgCl₂
                   [ 24.3 g Mg][1 mol Mg    ][ 1 mol MgCl₂  ]

2)  If  147.2 g of hexane combusts at 115C at 101.3KPa, how many liters of carbon dioxide will be produced?

                              2C₆H₁₄  +   19O₂  -->   12CO₂  +  14H₂O

[147.2 g C₆H₁₄ ][1 mol C₆H₁₄  ][12 mol  CO₂ ]   =  10.26 mol  CO₂
                          [86.1 g C₆H₁₄ ][2 mol  C₆H₁₄ ]     

 pv = nRt   v=nRt
                     p

v of  CO₂  =  [10.26 mol  ][ 8.31 KPa dm³][(115 + 273K)] = 327 dm³ CO₂
                      [101.3 KPa][         mol K    ]                          = 327 L CO₂

3) If 24L of oxygen reacts at STP with hydrogen, how many liters of water vapor will be produced?

                         O₂  + 2H₂  -->  2H₂O 

At STP one mole of any gas occupies the same volume (22.4 dm³) as one mole of any other gas.  Therefore, the molar ratios can be used to describe the relationship between volumes.  This applies ONLY at STP and only for gases.

                       [24 L O₂  ][ 2 mol H₂O ]  =  48 L H₂O
                                        [1 mol O₂]

longer way:

[24 L O₂  ][1 mol O₂ ][2 mol H₂O ][22.4 LH₂O ]  =  48 L H₂O
                 [22.4 L O₂][1 mol O₂     ][1 mol H₂O ]

gas laws

            Boyles, Charles, combined gas laws

4) My son's "dead" (flaccid) balloon which is 0.76 dm³ at 25C and 103 KPa, is heated it will bounce again.  What temperature is required to restore the balloon to it's original volume at standard pressure, 1.2L ? 

 p₁v₁t₂ = p₂v₂t₁

 p₁ 103 KPa
 v₁   0.76 dm³
 t₁    25 C + 273 = 298 K
 p₂   101.3 KPa
 v₂   1.2 dm³
 t₂   ???

   T =  [101.3 KPa][ 1.2 dm³   ][298 K]  =  464 K = 190 C
           [103 KPa   ][0.76 dm³ ] 

           ideal gas law

5) An excess of sulfuric acid reacts with 0.24g magnesium to produce hydrogen gas and a salt.  What volume of gas will be produced at 24C and 99.8KPa? 

                       H₂SO₄  +   Mg  -->  MgSO₄  +  H₂ 

   [0.024g Mg][1 mol Mg ][1 mol  H₂ ]  =  9.87E-4 mol H₂
                       [24.3 g Mg][1 mol Mg]

   pv = nRt   v=nRt
                        p

 v of  H₂  =  [9.87E-4 mol H₂  ][ 8.31 KPa dm³][(24 + 273K)] = 0.024 dm³ H₂
                    [99.8 KPa           ][         mol K    ]                          = 0.024 L H₂

periodic trends

6) Arrange the following elements and ions in ascending order by size:

Cl^-, Na, O, Ce, Ar.

  Cl 3p⁵  Cl^-  3p⁶      ion is bigger than atom
  Na 3p¹                  atom very small; smaller than Cl-
  O 2p⁴                    atom very small; smaller than Cl- and smaller than Na
                                it is in period before Na
  Ce 4f²                   in 4th period lanthanide series larger than Na and probably
                                larger than Cl- but not by much
  Ar  3p⁶                  noble gas in 3rd period  larger than all of the above

By Size:    O, Na, Cl^-,Ce, Ar

Rearrange those same elements (use Cl not Cl-) by reactivity from least reactive to most reactive.

  Cl 3p⁵                         highly reactive needs only 1 e-
  Na 3p¹                  highly reactive needs to lose 1 e-  smaller than Cl, more reactive
  O 2p⁴                    needs 2 e- more reactive than Cl, smaller than Cl
  Ce 4f²                    needs 2e-, and still not "noble" less reactive than all of above
  Ar  3p⁶                  noble gas needs no electrons  not reactive at all

Ar, Ce, Cl, Na, O

Rearrange those same elements by first ionization energy from least energy to greatest energy.

  Cl 3p⁵                         needs only 1 e-, very high first ionization energy
  Na 3p¹                  needs to lose 1 e-, low first ionization energy
  O 2p⁴                    needs 2 e- , smaller than Cl, higher first ionization energy than Cl
  Ce 4f²                    needs 2e-, and still not "noble"  higher first ionization energy than
                                Na, but not by much due to its' position within its level
  Ar  3p⁶                  noble gas needs no electrons  highest first ionization energy

Na, Ce, Cl, O, Ar

molecule shapes, bond angles, Lewis dot diagrams

7) What are the bond angles for octahedrals?

     octahedrals have 6 total pairs and 6 shared pairs; they have all 90^o angles

for irregular trigonal bipyramidal with 2 unshared pairs? 
             5 total pairs; 2 unshared pairs- this shape usually has 3 120^o angles and
              2 90o angles  the loss of  2 shared pairs makes this shape lose its 120^o angles;
              it is left with all 90^o angles

What are the bond angles for  a regular tetrahedral?
 4 total pairs; 4 shared pairs - 109.5^o angles

How many pairs does an irregular trigonal planar have total?
3 total pairs; 1 unshared pair

How many pairs does a regular trigonal bipyramidal have?
5 total pairs; 5 shared pairs

Draw PCl₃ and give shape and bond angles.

            P has 5 e- x 1 atom =  5
            Cl has 7e- x 3 atoms = 21
            total e                       = 26
           
            This forms an irregular tetrahedral.  It has 4 total pairs around the central
            atom and 1 of the pairs is unshared.  The bond angles will be less than
            109.5^o . 

nuclear chem

8) Write a balanced equation for each of the following.

a)  ⁹₃Li-->  ⁹₄ Be +_ ⁰_-1e__
b) ¹⁹⁹ ₈₄ Po + ⁰_-1e --> ¹⁹⁹₈₃Bi (K capture)
c) Beta minus emission by ³⁰₁₃Al  ___  ³⁰₁₃Al --> ⁰_-1e + ³⁰₁₄Si
d) Alpha emission by ²⁴²₉₄ Pu ______ ²⁴²₉₄ Pu --> ⁴₂ He + ²⁴⁰₉₂ U
e)  ¹⁴¹ ₆₂Sm--> ¹₁H + ¹⁴⁰ ₆₁Pm

9) How long will it take 6.00 x 10²⁰ atoms of ¹⁴⁵₆₄Gd to disintegrate to 1.88 x 10¹⁹ atoms if the half life of ¹⁴⁵₆₄Gd  is 25 minutes?

      1.88 x 10¹⁹ atoms  =  0.031
      6.00 x 10²⁰ atoms

      -(log 0.031) =  5 halflives
        (log 2)

        [5 halflives][ 25 min  ] =  125 min 
                         [ 1 halflife]

10) If the half-life of ¹²⁹₅₅Cs is 32.1 hours, how many atoms will be left after 5 days, 8 hours, 24 minutes if there were initially 1.00 mol of atoms?

     [5 days][24 hours] = 120 hours
                  [1 day     ]

     [24 min][1 hour ]   =   0.4 hours
                  [60 min]

     120 hours + 8 hours + .4 hours = 128.4 hours total time elapsed

     [128.4 hours][ 1 half life  ]  = 4 halflives  
                          [32.1 hours]

     1.00 mol * (1/2)⁴   =  1.00 mol * .0625  =  .0625 mol atoms remain