Jeff and Jill go canoeing. While reaching to feed a duck, the boat flips. Jeff and Jill blow
up their inflatable life preservers and then put
them on. As they wait for the rescue squad,
they calculate how much nitrogen is in each
life preserver. They estimate that the volume
is 13 L, pressurized to 1.2 atmat 25�C. The air
used for inflation is 80% nitrogen by volume
and 20% oxygen by volume. Give the amount
of nitrogen gas.
Answer in units of grams
You need clarify this. Give volume in what units and what pressure? Why wouldn't it be 80% of 1.2 atm?
To calculate the amount of nitrogen gas in the life preservers, we need to use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 25°C + 273.15 = 298.15 K
Next, let's convert the pressure from atm to pascals:
1 atm = 101325 Pa
P = 1.2 atm * 101325 Pa/atm = 121590 Pa
Now, let's calculate the number of moles of nitrogen using the ideal gas law:
n = PV / RT
Where:
P = pressure in pascals
V = volume in cubic meters
R = ideal gas constant = 8.314 J/(mol·K)
T = temperature in Kelvin
First, convert the volume from liters to cubic meters:
V = 13 L * (1 m^3 / 1000 L) = 0.013 m^3
Now, plug the values into the equation:
n = (121590 Pa * 0.013 m^3) / (8.314 J/(mol·K) * 298.15 K)
Calculate the result:
n ≈ 0.063 moles
Since the air used for inflation is 80% nitrogen by volume, we need to calculate the amount of nitrogen in moles:
moles of nitrogen = 0.063 moles * 0.80 = 0.0504 moles
Finally, we can calculate the amount of nitrogen gas in grams:
1 mole of nitrogen (N₂) has a molar mass of approximately 28 g/mol.
grams of nitrogen = moles of nitrogen * molar mass of nitrogen
grams of nitrogen = 0.0504 moles * 28 g/mol
grams of nitrogen ≈ 1.41 grams
Therefore, the amount of nitrogen gas in each life preserver is approximately 1.41 grams.