Question

An "empty" container is not really empty if it contains air. How may moles of nitrogen are in an "empty" two-liter cola bottle at atmospheric pressure and room temperature (25∘C25∘C)? Assume ideal behavior.

Express your answer to three significant figures and include the appropriate units.

Answer 1

To calculate the number of moles of nitrogen in the "empty" two-liter cola bottle, we need to consider that the air in the bottle consists of various gases, including nitrogen.

First, we'll find the volume of nitrogen in the bottle. At atmospheric pressure and room temperature (25°C), the volume of 1 mole of any ideal gas is approximately 22.7 liters (you can use the ideal gas law constant, R = 0.0821 L·atm/mol·K). Since the bottle is two liters, the volume of nitrogen would be:

Volume of nitrogen = Total volume of the bottle - Volume of other gases

Volume of nitrogen = 2 liters - 0 liters (since we assume it's an "empty" bottle)

Volume of nitrogen = 2 liters

Now, we can calculate the number of moles of nitrogen using the ideal gas law:

PV = nRT

where:

P = Pressure (atmospheric pressure) = 1 atm

V = Volume of nitrogen = 2 liters

n = Number of moles of nitrogen (what we want to find)

R = Ideal gas law constant = 0.0821 L·atm/mol·K

T = Temperature in Kelvin (25°C + 273.15) = 298.15 K

Now, solve for n (number of moles of nitrogen):

n = PV / RT

n = (1 atm) * (2 liters) / (0.0821 L·atm/mol·K * 298.15 K)

n ≈ 0.0842 moles

So, there are approximately 0.0842 moles of nitrogen in the "empty" two-liter cola bottle at atmospheric pressure and room temperature.