To find the volume of ethanol that contains the same number of molecules as 175 ml of water, we need to use the concept of molar volume.
The molar volume is the volume occupied by one mole of a substance. It is usually measured at standard conditions, which are a temperature of 273.15 K (0 °C) and a pressure of 1 atmosphere.
First, we need to convert the given volume of water (175 ml) to moles. Since the density of water is 1 g/ml, we know that 1 ml of water is equal to 1 gram. Therefore, the mass of 175 ml of water is 175 grams.
Next, we need to convert the mass of water to moles using the molar mass of water. The molar mass of water (H2O) is approximately 18 g/mol (2g/mol for hydrogen + 16 g/mol for oxygen).
Moles of water = Mass of water / Molar mass of water
Moles of water = 175 g / 18 g/mol
Moles of water ≈ 9.72 mol
Now, to find the volume of ethanol that contains the same number of molecules as 9.72 moles of water, we will use the molar volume concept.
The molar volume of a substance at standard conditions can be calculated using the equation:
Molar volume = (Volume of substance) / (Number of moles of substance)
We know the molar volume of water at standard conditions is 22.4 L/mol. Therefore, we can rearrange the equation to solve for the volume of ethanol:
Volume of ethanol = (Number of moles of ethanol) * (Molar volume of water)
To find the number of moles of ethanol, we can use the equation:
Number of moles of ethanol = (Number of moles of water) * (Molar mass of ethanol / Molar mass of water)
The molar mass of ethanol is approximately 46 g/mol.
Number of moles of ethanol ≈ 9.72 mol * (46 g/mol / 18 g/mol)
Number of moles of ethanol ≈ 24.78 mol
Finally, we can calculate the volume of ethanol:
Volume of ethanol = (Number of moles of ethanol) * (Molar volume of water)
Volume of ethanol ≈ 24.78 mol * 22.4 L/mol
Volume of ethanol ≈ 554.11 L
Therefore, the volume of ethanol that contains the same number of molecules as 175 ml of water is approximately 554.11 L.