1. Understanding the Basics
* Volume of a Cup: Let's assume a standard 8-ounce cup (about 237 ml).
* Water Density: Water has a density of approximately 1 gram per milliliter (g/ml). This means 1 ml of water weighs 1 gram.
* Molecular Weight of Water: A single water molecule (H₂O) has a molecular weight of 18 grams per mole.
2. The Calculations
* Mass of Water: Since 1 ml of water weighs 1 gram, our 237 ml cup contains 237 grams of water.
* Moles of Water: To find out how many moles of water are in the cup, we divide the mass by the molecular weight: 237 grams / 18 g/mol = 13.17 moles.
* Number of Molecules: One mole of any substance contains Avogadro's number of molecules (6.022 x 10²³). So, 13.17 moles of water contain: 13.17 moles * 6.022 x 10²³ molecules/mole = 7.93 x 10²⁴ molecules.
3. The Answer
It takes approximately 7.93 x 10²⁴ (7.93 septillion) water molecules to fill a standard 8-ounce cup!
Important Note: This is an approximation. The exact number will depend on the specific volume of the cup, the temperature of the water, and the definition of "fill" (whether it's completely full or leaving a small space at the top).
