Is there a database which give reaction constant?
The information you are looking for is out there, but sometimes you might have to work a little for it. 

The example reaction you post is a redox reaction. If we split the redox reaction into its two half-reactions, we can look up their reduction potentials (easier to find sometimes than equilibrium constants) and use the Nernst equation to calculate the equilibrium constant. I use Wikipedia for my list of standard potentials, but only because the values are identical to those in textbooks that I own. 


  Oxidation half-reaction


$$\ce{Fe^{2+} -&gt; Fe^{3+} + e-} \ \ \ E^\circ_{ox}= -0.77 \ \text{V}$$


  Reduction half-reaction


$$\ce{O2 + 4H+ + 4e- -&gt; 2H2O} \ \ \ E^\circ_{red} = +1.229 \ \text{V}$$


  Full balanced redox reaction


$$\ce{4Fe^{2+} + O2 +4H+ -&gt; 4Fe^{3+} + 2H2O}$$


  Cell potential


$$E^\circ_{cell}=E^\circ_{ox} + E^\circ_{red} = -0.77 \ \text{V} + 1.229 \ \text{V} = 0.459 \ \text{V}$$


  Nernst Equation


$$E^\circ_{cell}=\frac{RT}{zF}\ln{K_{eq}}$$

$$k_{eq}=e^{\dfrac{E^\circ_{cell}zF}{RT}}$$

In this equation, $z$ is the number of electrons transferred, $T$ is the temperature in kelvins, $R$ is the ideal gas constant, and $F$ is the Faraday constant. At 0 Celsius (273.15 K):

$$K_{eq}=e^{\dfrac{0.459 \ \text{V} \cdot 4\text{ mol}\cdot 96.49\times 10^3 \frac{\text{C}}{\text{mol}}}{ 8.314\ \frac{\text{J}}{\text{K}\cdot \text{mol}}\cdot 273.15\ \text{K} }}=7.565\times 10^{33}$$

If you can look up the enthalpy change or free energy change for the reaction (many of which are available at webbook.nist.gov/chemistry, then you can use a variant of the van 't Hoff equation

$$\Delta_r G^\circ = -RT\ln{K_{eq}}$$
$$K_{eq}=e^{\dfrac{-\Delta_R G^\circ}{RT}}$$