When more water is added, the liquid will become dilute. In this case, it also means that if the concentration is higher, there will be less water particles to block the hydrogen peroxide particles to meet up with the potatoes surface. Usually, if you double the concentration, you will half the reaction rate.
Hydrogen Peroxide.
Hydrogen Peroxide is a chemical compound of hydrogen and oxygen. As explained in My Investigation', its scientific formula is H2O2. If this solution has not been altered and is pure and anhydrous, it is colourless, slightly thick and has a gravity of 1.44. Although I do not think anyone would taste it, hydrogen peroxide has a metallic taste and will blister the skin. Concentrated solutions are unstable, and, if the liquid is still pure, it can explode when heated above a temperature over 100°C. Concentrations of hydrogen peroxide higher than 50 per cent can cause serious burns. Such factors as light, heat, chemical catalysts, dirt, and rust may cause hydrogen peroxide to decompose into water, oxygen, and heat. It is soluble in water. To keep hydrogen peroxide from decomposing, it is kept in dark bottles and at low temperatures.
Hydrogen peroxide is widely used in industry. It is manufactured in huge quantities by the electrolysis of aqueous solutions of sulfuric acid or of potassium bisulfate or ammonium bisulphate. Solutions containing 3 to 6 per cent hydrogen peroxide are used as antiseptics and germicides and as a skin cleanser. Higher concentrations are used in the manufacture of many chemical compounds. They also serve as bleaching agents for textiles and paper pulp, and as rocket propellants.
Hydrogen peroxide acts as both an oxidizing and reducing agent, because the oxygen freed in decomposition readily combines with other substances. Its oxidizing properties are used in bleaching thing such as hair, feathers, ivory and delicate fabrics e.g. wool, silk, nylon etc.