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 degrees celcius)? Assume ideal behavior.
To determine the number of moles of nitrogen in an "empty" two-liter cola bottle at atmospheric pressure and room temperature, we need to first understand the composition of air.
Atmospheric air primarily consists of nitrogen (approximately 78%), oxygen, carbon dioxide, and trace amounts of other gases. For simplicity, let's assume that air is made up of only nitrogen and oxygen.
Given that the bottle is "empty," we can consider it as being filled with air at atmospheric pressure. The ideal gas law, PV = nRT, relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T).
Since we are given the volume (V) of the two-liter cola bottle and the temperature (T) at room temperature (25 degrees Celsius), we can use the ideal gas law to solve for the number of moles of nitrogen.
Step 1: Convert temperature from Celsius to Kelvin
T(K) = 25 + 273.15
T(K) = 298.15 K
Step 2: Determine the ideal gas constant (R)
R = 0.0821 atm·L/mol·K (atm: atmospheres)
Step 3: Calculate the pressure (P)
At atmospheric pressure, we can assume it is approximately 1 atm.
Step 4: Rearrange the ideal gas law equation to solve for moles (n)
n = PV / RT
Substituting the values into the equation:
n = (1 atm) * (2 liters) / (0.0821 atm·L/mol·K) * (298.15 K)
Evaluating the equation:
n ≈ 0.0986 moles
Therefore, there are approximately 0.0986 moles of nitrogen in an "empty" two-liter cola bottle at atmospheric pressure and room temperature.