Good morning Roberta.
Are you sure that your system of equations makes sense physically?
What are you describing here?
What is the reason for (t -12) in the expression for dc/dt?
And when I rescale your amounts of material by dividing by 10^6 and let your code run I get an oscillatory behavior of concentration c ( which may well occur, see Belusov-Zhabotinsky -reaction), but it goes to negative values. But negative concentrations don't make sense.
Clear[a, b, c]
og = 15;
a0 = 1.2;
b0 = 0;
c0 = 2.6 10^1;
sol = NDSolve[
{Derivative[1][a][
t] == -0.001 a[t] + .03 a[t] (a0 - a[t] - b[t])/a0 -
0.0014 a[t] c[t],
Derivative[1][b][t] == -0.00257 b[t] + 0.0014 a[t] c[t],
Derivative[1][c][t] ==
482 (-12 + t) b[t] - 0.009` c[t] - 0.8 a[t] c[t],
a[0] == a0,
b[0] == 0,
c[0] == 2.6*10^1}, {a, b, c}, {t, 0, og},
MaxStepFraction -> 1/10000]
Plot[Evaluate[{a[t], b[t], c[t]} /. sol], {t, 0, og},
PlotRange -> All]