For the reaction
COBr2(g) → ← CO(g) + Br2(g)
Kc = 0.190 at 73 °C.
A reaction is run where the initial concentration of COBr2 is equal to the last 4 digits of your Student ID divided by 105 M. What are the equilibrium concentrations of all components?
Let the initial concentration of COBr2 be Ci = Last4StudentID/105
Solve the problem by writing the balanced reaction, writing the mass action expression, setting up a table of concentrations, substitute into the mass action expression, and solve. Then find each concentration using the solution.
COBr2(g) → ← CO(g) + Br2(g)
Kc = [CO]e[Cl2]e [COBr2]e = 0.190
InitialCi 0 0
Change–x +x +x
Equilibrium Ci – x x x
Substituting into the mass action expression and doing some algebra:
0.190 = x2/(Ci – x)
x2 + 0.190x – 0.190×Ci = 0.
This is solved using the quadratic equation and choosing the positive root.
Then [CO]e = [Br2]e = x and [COBr2]e = Ci – x.
Specific answers:
Last 4 digits Ci (M) [COBr2]e (M) [CO]e = [Br2]e (M)
0103 0.00103 0.00001 0.00102
0188 0.00188 0.00002 0.00186
0513 0.00513 0.00013 0.00500
0719 0.00719 0.00025 0.00694
0742 0.00742 0.00027 0.00715
0750 0.00750 0.00027 0.00723
0751 0.00751 0.00028 0.00723
0954 0.00954 0.00044 0.00910
1063 0.01063 0.0005 0.0101
1331 0.01331 0.0008 0.0125
1427 0.01427 0.0009 0.0133
1460 0.01460 0.0010 0.0136
1481 0.01481 0.0010 0.0138
1555 0.01555 0.0011 0.0145
1613 0.01613 0.0012 0.0150
1642 0.01642 0.0012 0.0152
1664 0.01664 0.0013 0.0154
1665 0.01665 0.0013 0.0154
1711 0.01711 0.0013 0.0158
1832 0.01832 0.0015 0.0168
1865 0.01865 0.0015 0.0171
1990 0.01990 0.0017 0.0182
2052 0.02052 0.0018 0.0187
2056 0.02056 0.0018 0.0187
2083 0.02083 0.0019 0.0189
2105 0.02105 0.0019 0.0191
2162 0.02162 0.0020 0.0196
2296 0.02296 0.0023 0.0207
2536 0.02536 0.0027 0.0227
2625 0.02625 0.0029 0.0234
2774 0.02774 0.0032 0.0246
2799 0.02799 0.0032 0.0248
2805 0.02805 0.0032 0.0248
2879 0.02879 0.0034 0.0254
2970 0.02970 0.0036 0.0261
2992 0.02992 0.0036 0.0263
3074 0.03074 0.0038 0.0269
3109 0.03109 0.0039 0.0272
3320 0.03320 0.0044 0.0288
3485 0.03485 0.0048 0.0301
3490 0.03490 0.0048 0.0301
3614 0.03614 0.0051 0.0311
3680 0.03680 0.0052 0.0316
3933 0.03933 0.0059 0.0334
3947 0.03947 0.0059 0.0335
4028 0.04018 0.0061 0.0341
4250 0.04250 0.0067 0.0358
4349 0.04349 0.0070 0.0365
4495 0.04495 0.0074 0.0375
4578 0.04578 0.0077 0.0381
4602 0.04602 0.0077 0.0383
5001 0.05001 0.0089 0.0411
5177 0.05177 0.0094 0.0423
5178 0.05178 0.0094 0.0423
5282 0.05282 0.0098 0.0431
5379 0.05379 0.0101 0.0437
5394 0.05394 0.0101 0.0438
5506 0.05506 0.0105 0.0446
5530 0.05530 0.0105 0.0448
5701 0.05701 0.0111 0.0459
5818 0.05818 0.0115 0.0467
5959 0.05959 0.0120 0.0476
6067 0.06067 0.0123 0.0484
6074 0.06074 0.0123 0.0484
6432 0.06432 0.0136 0.0508
6753 0.06753 0.0147 0.0528
6787 0.06787 0.0148 0.0531
6946 0.06946 0.0154 0.0541
6951 0.06951 0.0154 0.0541
6957 0.06957 0.0154 0.0541
6975 0.06975 0.0155 0.0543
6984 0.06984 0.0155 0.0543
7225 0.07225 0.0164 0.0558
7231 0.07231 0.0164 0.0559
7520 0.07520 0.0175 0.0577
7595 0.07595 0.0178 0.0582
7691 0.07691 0.0182 0.0587
7793 0.07793 0.0186 0.0594
7833 0.07833 0.0187 0.0596
7955 0.07955 0.0192 0.0604
8119 0.08119 0.0198 0.0614
8460 0.08460 0.0212 0.0634
8538 0.08538 0.0215 0.0639
8542 0.08542 0.0215 0.0639
8957 0.08957 0.0232 0.0664
9595 0.09595 0.0259 0.0701
9615 0.09615 0.0259 0.0702
9640 0.09640 0.0261 0.0704
9666 0.09666 0.0262 0.0705
9933 0.09933 0.0273 0.0720