Question

If the aquarium tank has a capacity of 50 gallons, how many molecules of oxygen gas can it hold? (hint: convert gallons to liters before you begin.) 1 gal = 3.79 L

Answer 1

First, let's convert gal to liters:

$50\text{ gal x( }\frac{3.79L}{1\text{ gal}})=189.5\text{ L}$

Let's assume this: as we work with oxygen gas, we consider STP conditions: 273.15 K (0 °C, 32 °F) and absolute pressure of exactly 1 atm (101.325 kPa). Nowadays we use 1 bar of pressure.

Another assumption is that oxygen gas is diluted as an O2 molecule.

Now we can do this:

At STP conditions for a gas:

1 mol of gas = 22.4 L = 6.022 x 10^23 formula units (formula units are molecules, atoms, etc.)

Procedure:

22.4 L of O2 -------- 6.022 x 10^23 molecules

189.5 L (50 gal) of O2 -------- x

$x\text{ = }\frac{189.5Lx6.022x10^{23}molecules}{22.4\text{ L}}=5.094x10^{24}molecules$

Answer: 5.094x10^24 molecules