A method for manufacturing a silica sol, the method comprising: 1) preparing a silica precursor composition, 2) preparing a catalyst composition, and 3) preparing the silica sol by mixing the silica precursor composition and the catalyst composition, wherein the silica precursor composition comprises a silica precursor, an organic solvent, and water, wherein the catalyst composition includes a hydrophobizing agent, a base catalyst, water, and an organic solvent, wherein the base catalyst is included in an amount of 0.4 parts by weight to 1.0 part by weight based on 100 parts by weight of the silica sol wherein the silica precursor in the silica precursor composition includes one or more selected from the group consisting of tetra methyl ortho silicate (TMOS), tetra ethyl ortho silicate (TEOS), methyl triethyl ortho silicate, dimethyl diethyl ortho silicate, tetra propyl ortho silicate, tetra isopropyl ortho silicate, tetra butyl ortho silicate, tetra secondarybutyl ortho silicate, tetra tertiarybutyl ortho silicate, tetra hexyl ortho silicate, tetra cyclohexyl ortho silicate, and tetra dodecyl ortho silicate, or a prehydrolysate of thereof, wherein the hydrophobizing agent comprises one or more selected from the group consisting of trimethylethoxysilane (TMES), trimethylsilanol, hexamethyldisiloxane (HMDSO), trimethylchlorosilane (TMCS), methyltrimethoxysilane (MTMS), methyltriethoxysilane (MTES), dimethyldiethoxysilane (DMDEOS), ethyltriethoxysilane, and phenyltriethoxysilane, wherein the organic solvent is selected from methanol, ethanol, isopropanol, butanol, glycerol, ethylene glycol, propylene glycol, diethylene glycol, dipropylene glycol, and sorbitol, or a mixture of two or more thereof, wherein the base catalyst is selected from sodium hydroxide, potassium hydroxide, ammonium hydroxide (NH4OH), tetramethylammonium hydroxide (TMAH), tetraethyl ammonium hydroxide (TEAH), tetrapropylammonium hydroxide (TPAH), tetrabutylammonium hydroxide (TBAH), methylamine, ethylamine, isopropylamine, monoisopropylamine, diethylamine, diisopropylamine, dibutylamine, trimethylamine, triethylamine, triisopropylamine, tributylamine, choline, monoethanolamine, diethanolamine, 2-aminoethanol, 2-(ethylamino) ethanol, 2-(methylamino) ethanol, N-methyldiethanolamine, dimethylaminoethanol, diethylaminoethanol, nitrilotriethanol, 2-(2-aminoethoxy)ethanol, 1-amino-2-propanol, triethanolamine, monopropanolamine, dibutanol, or a mixture of two or more thereof. 1) preparing a silica precursor composition, 2) preparing a catalyst composition, and 3) preparing the silica sol by mixing the silica precursor composition and the catalyst composition, wherein the silica precursor composition comprises a silica precursor, an organic solvent, and water, wherein the catalyst composition includes a hydrophobizing agent, a base catalyst, water, and an organic solvent, wherein the base catalyst is included in an amount of 0.4 parts by weight to 1.0 part by weight based on 100 parts by weight of the silica sol wherein the silica precursor in the silica precursor composition includes one or more selected from the group consisting of tetra methyl ortho silicate (TMOS), tetra ethyl ortho silicate (TEOS), methyl triethyl ortho silicate, dimethyl diethyl ortho silicate, tetra propyl ortho silicate, tetra isopropyl ortho silicate, tetra butyl ortho silicate, tetra secondarybutyl ortho silicate, tetra tertiarybutyl ortho silicate, tetra hexyl ortho silicate, tetra cyclohexyl ortho silicate, and tetra dodecyl ortho silicate, or a prehydrolysate of thereof, wherein the hydrophobizing agent comprises one or more selected from the group consisting of trimethylethoxysilane (TMES), trimethylsilanol, hexamethyldisiloxane (HMDSO), trimethylchlorosilane (TMCS), methyltrimethoxysilane (MTMS), methyltriethoxysilane (MTES), dimethyldiethoxysilane (DMDEOS), ethyltriethoxysilane, and phenyltriethoxysilane, wherein the organic solvent is selected from methanol, ethanol, isopropanol, butanol, glycerol, ethylene glycol, propylene glycol, diethylene glycol, dipropylene glycol, and sorbitol, or a mixture of two or more thereof, wherein the base catalyst is selected from sodium hydroxide, potassium hydroxide, ammonium hydroxide (NH4OH), tetramethylammonium hydroxide (TMAH), tetraethyl ammonium hydroxide (TEAH), tetrapropylammonium hydroxide (TPAH), tetrabutylammonium hydroxide (TBAH), methylamine, ethylamine, isopropylamine, monoisopropylamine, diethylamine, diisopropylamine, dibutylamine, trimethylamine, triethylamine, triisopropylamine, tributylamine, choline, monoethanolamine, diethanolamine, 2-aminoethanol, 2-(ethylamino) ethanol, 2-(methylamino) ethanol, N-methyldiethanolamine, dimethylaminoethanol, diethylaminoethanol, nitrilotriethanol, 2-(2-aminoethoxy)ethanol, 1-amino-2-propanol, triethanolamine, monopropanolamine, dibutanol, or a mixture of two or more thereof.