An empty water bottle is full of air at 15° C and standard pressure. The volume of the bottle is 0.500 liter. How many moles of air are in a bottle?

There are 0.0211 moles of air in the bottle

Explanation:

Step 1: Data given

Temperature of air = 15°C = 273.15 + 15 = 288.15 Kelvin

Standard pressure = 1 atm

Volume of the bottle = 0.500 L

Step 2: ideal gas law

p*V = n*R*T

with p = the pressure of the gas = 1 atm

with V = the volume of the bottle = 0.500 L

with n = the number of moles

with R = the gas constant = 0.08206 L*atm / mol*K

with T = the temperature of the gas = 15 °C = 288.15 Kelvin

In this case we have:

1atm * 0.500L = n * 0.08206 L*atm / mol*K * 288.15 K

Number of moles n = (1 atm * 0.500 L) / (0.08206 L*atm / mol*K * 288.15 K)

Number of moles = 0.0211 moles

There are 0.0211 moles of air in the bottle