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6. at the end of the 18th century, a kilogram was defined as the mass of exactly one cubic decimeter of water at the temperature where the density of water is at a maximum (now known to be 0.999972 g/cm³ at 3.98 °c and 1 atm pressure, see http://www.sizes.com/units/kilogram.htm). How many moles of water is this? solve everything step by step cancelation to cancelation gen chem
Accepted Answer
Here's the step-by-step calculation to determine the moles of water in one kilogram:
1. Convert volume to cubic centimeters:
- One cubic decimeter (dm³) is equal to 1000 cubic centimeters (cm³).
2. Calculate the mass of water:
- Density = Mass / Volume
- Mass = Density x Volume
- Mass = 0.999972 g/cm³ x 1000 cm³ = 999.972 g
3. Convert mass to grams:
- 1 kilogram (kg) = 1000 grams (g)
4. Calculate the moles of water:
- Moles = Mass / Molar Mass
- Molar Mass of water (H₂O) = 18.015 g/mol
- Moles = 999.972 g / 18.015 g/mol = 55.508 moles
Therefore, one kilogram of water at its maximum density contains approximately 55.508 moles of water.
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