Why is snow white and water transparent but sometimes ice can be both?

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Many gases including carbon dioxide, oxygen, nitrogen, hydrogen are soluble in water. For example solubility of oxygen & nitrogen in water at room temperature (25 degree C) are 0.0089 g/litre & 0.0138 g/litre. According to Henry's law, gas solubility in water increase as the temperature decrease. Water droplets at very high altitude with low temperature environment have high solubility for gas. Besides, the small water droplets have very high surface area for gas to dissolve.

Hence, water droplets in cloud are saturated with dissolved gases. When the environment temperature decrease until freezing point, gas which is not soluble in snow will trap in side and form tiny bubble. The size and the distribution of the tiny bubble are quite uniform due to small droplet size and fast freezing rate. Visible light reflected by tiny bubble give white color snow.

Water is transparent because it doesn't absorb or reflect visible light.

The appearance of cloudy ice is normally depend on water properties and method of making the ice. Tiny bubble trap in ice will give white color. Ice normally has size much bigger than water droplet in cloud (low surface area to size ratio). In a cube of water, water near its surface will freeze first. Bubble will move towards the center of ice and form cloudy part at the center.

Water which has undergone process that remove dissolved gases will not become cloudy ice. For example: deaeration by boiling water at 100 degree C. The reason ice cubes you by in the market, hotels, and bars are clear is that the freezing takes place in a flow of water over a cold surface. Then the minerals and air are continuously washed away and pure ice forms clear ice cubes.

Sometimes, water or ice is blue color (ocean or iceberg) because it absorbs slightly of the red-frequency part of visible light (Insignificant Normally).

References:

Why is Snow White and Water Transparent but Sometimes Ice can be Both? life Chemistry. Retrieved June 19, 2008, from http://life-chemistry.blogspot.com/2008/06/why-is-snow-white-and-water-transparent.html

Air Solubility in Water. The Engineering Tool Box. Retrieved June 19, 2008, from http://www.engineeringtoolbox.com/air-solubility-water-d_639.html

Henry's Law. Wikipedia. Retrieved June 19, 2008, from http://en.wikipedia.org/wiki/Henry\'s_law

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