Oxygen Drawn from a Cylinder

Q. An oxygen cylinder of volume 30 L has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. The molecular mass of O2 is 32 g/mol. Estimate the mass of oxygen taken out of the cylinder, in kilograms? expects 0.14 kg

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. An oxygen cylinder $V_{l} = V_{f}$ of volume 30 L $V_{f} = 30$ L has an initial gauge pressure of 15 atm $P_{f} = 15$ atm and a temperature of 27 °C $T_{f} = 300$ K. After some oxygen $M_{w} = M_{f}$ is withdrawn from the cylinder $n_{w} = n_{f} - n_{l}$ , the gauge pressure drops to 11 atm $P_{l} = 11$ atm and its temperature drops to 17 °C $T_{l} = 290$ K. The molecular mass of O2 is 32 g/mol $M_{f} = 32$ g/mol. Estimate the mass of oxygen taken out of the cylinder, in kilograms?

The playground

Inputs

volume

V_{f}

30 L

initial pressure

P_{f}

15 atm

final pressure

P_{l}

11 atm

molar mass

M_{f}

32 g/mol

Outputs

mass

m_{w}

The solution

Solved with Moles

Given

$V_{f} = 30$ L
$P_{f} = 15$ atm
$P_{l} = 11$ atm
$M_{f} = 32$ g/mol
$T_{f} = 300$ K from “a temperature of 27 °C”
$T_{l} = 290$ K from “drops to 17 °C”
$V_{l} = V_{f}$ from “An oxygen cylinder”
$M_{w} = M_{f}$ from “some oxygen”
$n_{w} = n_{f} - n_{l}$ from “withdrawn from the cylinder”

Find $m_{w}$ .

Working

$V_{f} = 30$ L $= 0.03$ m³
$P_{f} = 15$ atm $= 1.519875 \times 10^{6}$ Pa
$P_{l} = 11$ atm $= 1.114575 \times 10^{6}$ Pa
$M_{f} = 32$ g/mol $= 0.032$ kg/mol
ideal gas law(full) $P_{f} \cdot V_{f} = n_{f} \cdot R \cdot T_{f}$
$1.519875 \times 10^{6} \cdot 0.03 = n_{f} \cdot 8.31446262 \cdot 300$
$n_{f} = 18.2798946$ mol
An oxygen cylinder $V_{l} = V_{f}$
$V_{l} = 0.03$
$V_{l} = 0.03$ m³
ideal gas law(left) $P_{l} \cdot V_{l} = n_{l} \cdot R \cdot T_{l}$
$1.114575 \times 10^{6} \cdot 0.03 = n_{l} \cdot 8.31446262 \cdot 290$
$n_{l} = 13.8675062$ mol
withdrawn from the cylinder $n_{w} = n_{f} - n_{l}$
$n_{w} = 18.2798946 - 13.8675062$
$n_{w} = 4.41238834$ mol
some oxygen $M_{w} = M_{f}$
$M_{w} = 0.032$
$M_{w} = 0.032$ kg/mol
mass of a gas(withdrawn) $m_{w} = n_{w} \cdot M_{w}$
$m_{w} = 4.41238834 \cdot 0.032$
$m_{w} = 0.1412$ kg
$m_{w} \approx 0.14$ kgto 2 significant figures

Conclusion

The cylinder keeps its volume, so the ideal gas law counts the moles in it before and after; the moles missing, times the mass of a mole, went out with the oxygen drawn.

The Ruby

1require_relative "../physics"23question :oxygen_drawn_from_a_cylinder do4  kind :numerical5  describes "An oxygen cylinder of volume %{volume} has an initial gauge pressure of %{initial_pressure} and a " \6            "temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to " \7            "%{final_pressure} and its temperature drops to 17 °C. The molecular mass of O2 is %{molar_mass}. %{mass}, " \8            "in kilograms?"9  given volume: "30 L"10  given initial_pressure: "15 atm"11  given final_pressure: "11 atm"12  given molar_mass: "32 g/mol"13  asks mass: "Estimate the mass of oxygen taken out of the cylinder"14end

1require_relative "../questions/oxygen_drawn_from_a_cylinder"2require_relative "../science/kinetic_theory/moles"34solve :oxygen_drawn_from_a_cylinder, using: Moles do5  objects :full, :left, :withdrawn67  take volume: full.volume8  take initial_pressure: full.pressure9  take final_pressure: left.pressure10  take molar_mass: full.molar_mass1112  deduce_from "a temperature of 27 °C", full.temperature => "300 K"13  deduce_from "drops to 17 °C", left.temperature => "290 K"14  deduce_from "An oxygen cylinder", left.volume => full.volume15  deduce_from "some oxygen", withdrawn.molar_mass => full.molar_mass16  deduce_from "withdrawn from the cylinder", withdrawn.amount => full.amount - left.amount1718  mass = withdrawn.mass19  answer mass:, in: "kg", figures: 22021  conclusion "The cylinder keeps its volume, so the ideal gas law counts the moles in it before and after; the " \22             "moles missing, times the mass of a mole, went out with the oxygen drawn."23end

1require_relative "../solutions/oxygen_drawn_from_a_cylinder"23play_with :oxygen_drawn_from_a_cylinder do4  title "Oxygen Drawn from a Cylinder"5end

The laws

quantity	written	units	within	from
gas constant	$R$	J mol⁻¹ K⁻¹	—	IdealGas
pressure	$P$	Pa	0 … ∞	IdealGas
volume	$V$	m³	0 … ∞	IdealGas
amount	$n$	mol	—	IdealGas
temperature	$T$	K	0 … 1e+09	IdealGas
molar mass	$M$	kg/mol	—	IdealGas
density	$ρ$	kg/m³	0 … ∞	IdealGas
avogadro constant	$N_{A}$	mol⁻¹	—	Moles
mass	$m$	kg	0 … ∞	Moles
molecules	$N$	—	—	Moles
pressure of ground	$P_{g}$	Pa	0 … ∞
volume of ground	$V_{g}$	m³	0 … ∞
amount of ground	$n_{g}$	mol	—
temperature of ground	$T_{g}$	K	0 … 1e+09
pressure of full	$P_{f}$	Pa	0 … ∞
volume of full	$V_{f}$	m³	0 … ∞
amount of full	$n_{f}$	mol	—
temperature of full	$T_{f}$	K	0 … 1e+09
pressure of left	$P_{l}$	Pa	0 … ∞
volume of left	$V_{l}$	m³	0 … ∞
amount of left	$n_{l}$	mol	—
temperature of left	$T_{l}$	K	0 … 1e+09
pressure of withdrawn	$P_{w}$	Pa	0 … ∞
volume of withdrawn	$V_{w}$	m³	0 … ∞
amount of withdrawn	$n_{w}$	mol	—
temperature of withdrawn	$T_{w}$	K	0 … 1e+09
density of ground	$ρ_{g}$	kg/m³	0 … ∞
molar mass of ground	$M_{g}$	kg/mol	—
density of full	$ρ_{f}$	kg/m³	0 … ∞
molar mass of full	$M_{f}$	kg/mol	—
density of left	$ρ_{l}$	kg/m³	0 … ∞
molar mass of left	$M_{l}$	kg/mol	—
density of withdrawn	$ρ_{w}$	kg/m³	0 … ∞
molar mass of withdrawn	$M_{w}$	kg/mol	—
mass of ground	$m_{g}$	kg	0 … ∞
mass of full	$m_{f}$	kg	0 … ∞
mass of left	$m_{l}$	kg	0 … ∞
mass of withdrawn	$m_{w}$	kg	0 … ∞
molecules of ground	$N_{g}$	—	—
molecules of full	$N_{f}$	—	—
molecules of left	$N_{l}$	—	—
molecules of withdrawn	$N_{w}$	—	—

P_{g} \cdot V_{g} = n_{g} \cdot R \cdot T_{g}

ideal gas law

ρ_{g} = \frac{n_{g} \cdot M_{g}}{V_{g}}

density of a gas

m_{g} = n_{g} \cdot M_{g}

mass of a gas

N_{g} = n_{g} \cdot N_{A}

molecules in a gas

P_{g} \cdot V_{g} = n_{g} \cdot R \cdot T_{g}

ideal gas law(ground)

P_{f} \cdot V_{f} = n_{f} \cdot R \cdot T_{f}

ideal gas law(full)

P_{l} \cdot V_{l} = n_{l} \cdot R \cdot T_{l}

ideal gas law(left)

P_{w} \cdot V_{w} = n_{w} \cdot R \cdot T_{w}

ideal gas law(withdrawn)

ρ_{g} = \frac{n_{g} \cdot M_{g}}{V_{g}}

density of a gas(ground)

ρ_{f} = \frac{n_{f} \cdot M_{f}}{V_{f}}

density of a gas(full)

ρ_{l} = \frac{n_{l} \cdot M_{l}}{V_{l}}

density of a gas(left)

ρ_{w} = \frac{n_{w} \cdot M_{w}}{V_{w}}

density of a gas(withdrawn)

m_{g} = n_{g} \cdot M_{g}

mass of a gas(ground)

m_{f} = n_{f} \cdot M_{f}

mass of a gas(full)

m_{l} = n_{l} \cdot M_{l}

mass of a gas(left)

m_{w} = n_{w} \cdot M_{w}

mass of a gas(withdrawn)

N_{g} = n_{g} \cdot N_{A}

molecules in a gas(ground)

N_{f} = n_{f} \cdot N_{A}

molecules in a gas(full)

N_{l} = n_{l} \cdot N_{A}

molecules in a gas(left)

N_{w} = n_{w} \cdot N_{A}

molecules in a gas(withdrawn)

V_{l} = V_{f}

An oxygen cylinder

M_{w} = M_{f}

some oxygen

n_{w} = n_{f} - n_{l}

withdrawn from the cylinder