How many molecules of water needs to be in a container at STP (standard temperature and pressure) does it take to exhibit the visual properties of liquid?
Discussion
For water to exhibit visual properties of a liquid, such as being visible to the human eye and forming droplets, you would need a significant number of water molecules. The exact number is difficult to quantify precisely without delving into the specifics of what constitutes "visual properties" of a liquid. If we're discussing the ability to form a droplet that is visible to the naked eye, we're talking about scales much larger than molecular.
A rough estimate can be made by considering the smallest volume of water that can be perceived as a droplet by the human eye. Let's assume a droplet is about \(0.05\) mL (or \(5 \times 10^{-8}\) m\(^3\)), which is a reasonable lower bound for what we might visually recognize as a droplet of water.
Given that the molar volume of an ideal gas (and by approximation, of liquid water under STP conditions) is about \(22.4\) L/mol, and considering the molecular weight of water (\(H_2O\)) is approximately \(18\) g/mol, we can calculate the number of molecules in a \(0.05\) mL droplet of water.
First, calculate the number of moles in \(0.05\) mL of water:
\[ \text{Volume of water} = 0.05 \, \text{mL} = 5 \times 10^{-5} \, \text{L} \]
\[ \text{Density of water} = 1 \, \text{g/mL} = 1000 \, \text{g/L} \]
\[ \text{Mass of water} = \text{Volume of water} \times \text{Density of water} = 5 \times 10^{-5} \, \text{L} \times 1000 \, \text{g/L} = 5 \times 10^{-2} \, \text{g} \]
\[ \text{Number of moles} = \frac{\text{Mass of water}}{\text{Molar mass of water}} = \frac{5 \times 10^{-2} \, \text{g}}{18 \, \text{g/mol}} \]
Next, calculate the number of molecules, using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol):
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
Let's calculate the number of molecules now.
To exhibit the visual properties of a liquid, such as forming a visible droplet, you would need approximately \(1.67 \times 10^{21}\) water molecules at standard temperature and pressure (STP). This estimate is based on the smallest volume of water that can be visually recognized as a droplet.
1,432,612
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Depends on the size of the container ¯\_(ツ)_/¯
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