Perfect Ratio for Solidifying Water: Liquid Nitro vs Water | Simplified Equation

[mtanti]

What ratio of liquid nitrogen to water must there be for total solidification of water (@ RTP)? If there is no static ratio a simplified equation would be nice...
10x!

 

[Gokul43201]

This is a simple energy conservation problem, and might even be homework.

Find the latent heats and the (average/integrated) heat capacity of LN2 from 77K to 273K and use the fact that, under ideal conditions, heat lost by water during cooling and solidification equals the heat gained by LN2 during boiling and warming up (assuming there is still thermal contact between the cold gas and the water - this is unknown as the experimental conditions remain unspecified; else ignore the warming term).

 

[charng]

I would first like to clarify that the term "total solidification" is not scientifically accurate. Water can never be completely solidified, as it is always in a state of dynamic equilibrium between solid and liquid phases at room temperature and pressure (RTP).

That being said, the ratio of liquid nitrogen to water needed for the majority of the water to solidify at RTP can be approximated using the simplified equation:

Ratio of liquid nitrogen to water = (molar mass of water/ molar mass of liquid nitrogen) * (heat of fusion of water/ heat of vaporization of liquid nitrogen)

This equation takes into account the molar masses and heat of fusion/vaporization of water and liquid nitrogen, which are important factors in determining the amount of energy needed for solidification to occur.

However, it is important to note that this is a simplified equation and may not account for all variables that could affect the solidification process. The exact ratio may vary depending on factors such as temperature, pressure, and impurities in the water.

In conclusion, while a simplified equation can provide an estimate of the ratio of liquid nitrogen to water for solidification at RTP, further experimentation and analysis would be needed to determine the most accurate and precise ratio for a specific scenario.