# What are the gas laws formulas?

Dec 17, 2017

There are a few

#### Explanation:

Boyle's law:
$P \propto \frac{1}{V}$

Charles' law:
$V \propto T$

Pressure law:
$P \propto T$

$V \propto n$

Ideal gas law:
$P V = n R T$ or $P V = N k T$

These may also apply:
$P V = \frac{N m < {c}^{2} >}{3}$ and $\frac{1}{2} m < {c}^{2} \ge \frac{3}{2} k T = \frac{3}{2} \frac{R T}{{N}_{a}}$

Key:
$P$ = pressure ($P a$)
$V$ = volume (${m}^{3}$)
$T$ = absolute temperature ($K$)
$n$ = number of moles ($m o l$)
$R$ = gas constant (N_a*k) ($8.31 J \textcolor{w h i t e}{l} {K}^{- 1} \textcolor{w h i t e}{l} m o {l}^{- 1}$)
$N$ = number of atoms/molecules ($n \cdot {N}_{a}$)
$k$ = Boltzmann constant ($1.38 \cdot {10}^{- 23} J \textcolor{w h i t e}{l} {K}^{- 1}$)
$m$ = mass of one atom/molecule ($k g$)
$< {c}^{2} >$ = root-mean-squared speed of atoms/molecules ($\sqrt{\frac{{a}^{2} + {b}^{2} + {c}^{2} + \cdots}{N}}$) ($m {s}^{- 1}$)

Dec 17, 2017

You only need one for ideal gases:

$\textcolor{b l u e}{| \overline{\underline{\stackrel{\text{ ")(" "PV = nRT" }}{|}}}}$

where:

• $P$ is pressure in $\text{atm}$.
• $V$ is volume in $\text{L}$.
• $n$ is mols of ideal gas.
• $R = \text{0.082057 L"cdot"atm/mol"cdot"K}$ is the universal gas constant for these pressure and volume units.
• $T$ is the temperature in $\text{K}$.

If you wish to utilize other ones, you must examine the question wording and determine the environmental conditions, then set up your initial and final states. This is how you will be expected to do it on exams.

CONSTANT PRESSURE AND MOLS OF GAS

In this case your volume and temperature vary.

$P {V}_{1} = n R {T}_{1}$
$P {V}_{2} = n R {T}_{2}$

Thus, dividing these gives

${V}_{1} / {V}_{2} = {T}_{1} / {T}_{2}$

or

$\textcolor{b l u e}{{V}_{1} / {T}_{1} = {V}_{2} / {T}_{2}}$,

known as Charles's Law.

CONSTANT TEMPERATURE AND MOLS OF GAS

In this case your pressure and volume vary.

${P}_{1} {V}_{1} = n R T$
${P}_{2} {V}_{2} = n R T$

Thus, we get

$\textcolor{b l u e}{{P}_{1} {V}_{1} = {P}_{2} {V}_{2}}$,

known as Boyle's Law.

CONSTANT PRESSURE AND TEMPERATURE

In this case your volume and mols vary such that your molar volume is constant for the same gas:

$P {V}_{1} = {n}_{1} R T$
$P {V}_{2} = {n}_{2} R T$

Therefore,

${V}_{1} / {V}_{2} = {n}_{1} / {n}_{2}$

or

$\textcolor{b l u e}{{V}_{1} / {n}_{1} \equiv {\overline{V}}_{1} = {V}_{2} / {n}_{2} \equiv {\overline{V}}_{2}}$

otherwise known as Avogadro's principle.

CONSTANT VOLUME AND MOLS OF GAS

Here we have varying pressure and temperature:

${P}_{1} V = n R {T}_{1}$
${P}_{2} V = n R {T}_{2}$

Thus,

${P}_{1} / {P}_{2} = {T}_{1} / {T}_{2}$

or

$\textcolor{b l u e}{{P}_{1} / {T}_{1} = {P}_{2} / {T}_{2}}$

sometimes known as Gay-Lussac's Law.