# How Many Molecules Are in a Glass of Water?

The number of molecules in a glass of water can be quickly calculated knowing only the total weight of the water, including any ice cubes. If you don't know the weight, but you know both the volume and temperature of liquid water, you can still accurately estimate the number of molecules. To use this second method, you must look up the density of liquid water at a certain temperature, then multiply the density and the volume to find the weight.

The equation to calculate the number of water molecules, **N** is

N = A*W/18.01528

where **A** is Avogadro's constant equal to 6.0221415×10²³ (one mole), **W** is the weight of the water in grams, and 18.01528 is the molecular weight of water. (I.e., one mole of water weighs 18.01528 grams.)

You can use the calculator on the left to quickly compute the number of molecules in a glass of water, or work it out by hand.

**Example 1:** A glass of ice water with weighs 283.5 grams, not including the cup that holds it. To estimate the number of water molecules in the glass, compute

(6.0221415 × 10²³)(283.5)/18.01528

= [(6.0221415)(283.5)/18.01528]10²³

= 94.7682809 × 10²³

= 9.47682809 × 10²⁴.

**Example 2:** A glass contains 140 mL of water at a temperature of 50.3°C. Since the density of water at this temperature is about 0.9879034 g/mL, the total weight of the water is

(140 mL)(0.9879034 g/mL) = 138.306476 g.

Now you can figure the number of molecules:

(6.0221415 × 10²³)(138.306476)/18.01528

= [(6.0221415)(138.306476)/18.01528]10²³

= 46.2330404 × 10²³

= 4.62330404 × 10²⁴.

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