Methods of preparing a catalyst

1. A hydrogel comprising:

water; and

an agglomeration of titanium-silica-chromium nanoparticle, wherein each titanium-silica-chromium nanoparticle agglomerate is an agglomeration of titanium-silica-chromium nanoparticles, the agglomerates having an average titanium penetration depth designated x with a coefficient of variation for the average titanium penetration depth of less than about 1.0 wherein a silica content of the hydrogel is of from about 18 wt. % to about 35 wt. % based on a total weight of the hydrogel;

wherein the titanium content is from about 0.15 wt. % to about 1.5 wt. % based on the total weight of the hydrogel; and

wherein the chromium content is from about 0.15 wt. % to about 1.2 wt. % based on the total weight of the hydrogel.

2. The hydrogel of claim 1 wherein the titanium-silica-chromium nanoparticles have a coefficient of variation of the average titanium penetration depth from about 0.1 to about 0.9.

3. The hydrogel of claim 1 having a mL pore water in the pores of the hydrogel, per g of silica of from about 1.9 cm 3 /g to about 4.6 cm 3 /g.

4. The hydrogel of claim 1 wherein a coefficient of variation for an average particle size of the titanium-silica-chromium nanoparticle is less than about 1.

5. The hydrogel of claim 1 having an x value ranging from about 0.25 wt. % to about 8 wt. % based on the total weight of the hydrogel.

6. The hydrogel of claim 1 having a titanium coverage of from about 1 titanium atoms/nm 2 to less than about 4 titanium atoms/nm 2 .

7. The hydrogel of claim 1 having a mL pore water in the pores of the hydrogel, per g of silica of from about 2.3 cm 3 /g to about 5.6 cm 3 /g.

8. The hydrogel of claim 1 wherein the titanium-silica-chromium nanoparticle comprises an acid-soluble titanium-containing compound.

9. The hydrogel of claim 8 wherein the acid-soluble titanium-containing compound comprises a trivalent titanium, tetravalent titanium, titania, or a combination thereof.

10. The hydrogel of claim 8 wherein the acid-soluble titanium-containing compound comprises TiCl 4 , TiOSO 4 , TiBr 4 , TiOCl 2 , TiOBr 2 , TiO 2 , TiO(oxylate) 2 , or a combination thereof.

11. The hydrogel of claim 8 wherein the acid-soluble titanium-containing compound comprises Ti 2 (SO 4 ) 3 , Ti(OAc) 3 , Ti(oxylate) 3 , Ti(NO 3 ) 3 , or a combination thereof.

12. The hydrogel of claim 1 wherein the titanium-silica-chromium nanoparticle comprises a water-soluble chromium compound, a hydrocarbon-soluble chromium compound, or a combination thereof.

13. The hydrogel of claim 12 wherein the titanium-silica-chromium nanoparticle comprises a chromium (II) compound, a chromium (III) compound, or a combination thereof.

14. The hydrogel of claim 12 wherein the titanium-silica-chromium nanoparticle comprises chromium carboxylates, chromium naphthenates, chromium halides, chromium pyrrolides, chromium benzoates, chromium dionates, chromium nitrates, chromium sulfates, or a combination thereof.

15. The hydrogel of claim 12 wherein the titanium-silica-chromium nanoparticle comprises chromium (III) isooctanoate, chromium (III) 2,2,6,6-tetramethylheptanedionate, chromium (III) naphthenate, chromium (III) chloride, chromium (III) tris(2-ethylhexanoate), chromic fluoride, chromium (III) oxy-2-ethylhexanoate, chromium (III) dichloroethylhexanoate, chromium (III) acetylacetonate, chromium (III) acetate, chromium (III) butyrate, chromium (III) neopentanoate, chromium (III) laurate, chromium (III) sulfate, chromium (III) oxalate, chromium (III) benzoate, chromium (III) pyrrolide(s), chromium (III) perchlorate, chromium (III) chlorate, or a combination thereof.

16. The hydrogel of claim 12 wherein the titanium-silica-chromium nanoparticle comprises chromous fluoride, chromous chloride, chromous bromide, chromous iodide, chromium (II) bis(2-ethylhexanoate), chromium (II) acetate, chromium (II) butyrate, chromium (II) neopentanoate, chromium (II) laurate, chromium (II) stearate, chromium (II) oxalate, chromium (II) benzoate, chromium (II) pyrrolide(s), chromous sulfate, or a combination thereof.

17. The hydrogel of claim 12 wherein the titanium-silica-chromium nanoparticle comprises tertiary butyl chromate in a hydrocarbon liquid; chromium trioxide in water; chromium acetate in water; chromium nitrate in alcohol; zerovalent organochromium or a combination thereof.

18. The hydrogel of claim 1 formed from an acidic titanium solution.

19. The hydrogel of claim 18 wherein the acid comprises hydrochloric acid, hydrobromic acid, sulfuric acid, nitric acid, phosphoric acid, perchloric acid, sulfamic acid, or a combination thereof.