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 18 L, pressurized to 1.4 atm at 25◦C. The air used for inflation is 80% nitrogen by volume.

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VestaHofman VestaHofman · Answer 1 · 2019-12-12T11:49:23+01:00

Answer:

The amount nitrogen gas in the given balloon = 23.07 g

Explanation:

Given: Total volume of balloon: V = 18 L, Pressure = 1.4 atm, Temperature = 25°C = 25 + 273 = 298K (∵ 0°C = 273 K)

Volume of Nitrogen gas in balloon: V₁ = V × 80% = 18 L × (80 / 100) = 14.4 L

Molar mass of nitrogen gas (N₂): M = 28 g/mol

According to the ideal gas law:

PV= nRT

Here, Gas constant: R = 0.08206 L·atm/(mol·K)

n = total number of moles of gas

P = Pressure in atm

T = Temperature in K

V = Volume in L

Therefore, the number of moles of oxygen gas (n₁) is given by:

[tex]\Rightarrow n_{1} = \frac{PV_{1}}{RT}[/tex]

[tex]n_{1} = \frac{1.4 atm\times 14.4 L}{0.08206 L.atm/(mol.K)\times298K}[/tex]

[tex]n_{1} = 0.824 mole[/tex]

As number of moles: [tex]n = \frac{mass}{Molar\, mass}[/tex]

[tex]\Rightarrow Mass\, of \, nitrogen \, gas = n_{1} \times M = 0.824 mol \times 28 g/mol = 23.07 g[/tex]

Therefore, the amount nitrogen gas in the given balloon = 23.07 g