Molar Volume at STP

Q. Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure, 0 °C). What is the molar volume, in litres? expects 22.4 L

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The web of concepts

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The equations it used

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Q. Molar volume is the volume occupied by 1 mol $n = 1$ mol of any (ideal) gas at standard temperature and pressure (STP : 1 atmospheric pressure $P = 1$ atm, 0 °C $T = 273.15$ K). What is the molar volume, in litres?

The playground

Inputs

amount

n

1 mol

Outputs

volume

V

The solution

Solved with IdealGas

Given

$n = 1$ mol
$P = 1$ atm from “1 atmospheric pressure”
$T = 273.15$ K from “0 °C”

Find $V$ .

Working

$P = 1$ atm $= 101325$ Pa
ideal gas law(gas) $P \cdot V = n \cdot R \cdot T$
$101325 \cdot V = 1 \cdot 8.31446262 \cdot 273.15$
$V = 22.41$ L
$V = 0.0224139695$ m³ $= 22.4139695$ L
$V \approx 22.4$ Lto 3 significant figures

Conclusion

The ideal gas law has no room for what the molecules are, so a mole of any gas at the same pressure and temperature takes up the same volume.

The Ruby

1require_relative "../physics"23question :molar_volume_at_stp do4  kind :numerical5  describes "Molar volume is the volume occupied by %{amount} of any (ideal) gas at standard temperature and pressure " \6            "(STP : 1 atmospheric pressure, 0 °C). %{volume}, in litres?"7  given amount: "1 mol"8  asks volume: "What is the molar volume"9end

1require_relative "../questions/molar_volume_at_stp"2require_relative "../science/kinetic_theory/ideal_gas"34solve :molar_volume_at_stp, using: IdealGas do5  objects :gas67  take amount: gas.amount89  deduce_from "1 atmospheric pressure", gas.pressure => "1 atm"10  deduce_from "0 °C", gas.temperature => "273.15 K"1112  volume = gas.volume13  answer volume:, in: "L", figures: 31415  conclusion "The ideal gas law has no room for what the molecules are, so a mole of any gas at the same pressure " \16             "and temperature takes up the same volume."17end

1require_relative "../solutions/molar_volume_at_stp"23play_with :molar_volume_at_stp do4  title "Molar Volume at STP"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
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 gas	$P$	Pa	0 … ∞
volume of gas	$V$	m³	0 … ∞
amount of gas	$n$	mol	—
temperature of gas	$T$	K	0 … 1e+09
density of ground	$ρ_{g}$	kg/m³	0 … ∞
molar mass of ground	$M_{g}$	kg/mol	—
density of gas	$ρ$	kg/m³	0 … ∞
molar mass of gas	$M$	kg/mol	—

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

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

ideal gas law(ground)

P \cdot V = n \cdot R \cdot T

ideal gas law(gas)

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

density of a gas(ground)

ρ = \frac{n \cdot M}{V}

density of a gas(gas)