Question

A 75.0-g sample of dinitrogen monoxide is confined in a 3.1-L vessel. What is the pressure (in atm) at $\mathbf{115}\mathbf{°}\mathit{C}$?

Short answer

Answer

The pressure of the given gas is 17.47 atm.

Step-by-step solution

Ideal gas law

The ideal gas law equation is,

$\mathit{P}\mathit{V}\mathbf{=}\mathit{n}\mathit{R}\mathit{T}$

The ideal gas law for the given condition can be written as,

$\mathit{P}\mathbf{=}\frac{\mathbf{nRT}}{\mathbf{V}}$

Here,

V is the volume (3.1 L)

T is the temperature ($\mathbf{115}\mathbf{°}\mathit{C}\mathbf{=}\mathbf{388}\mathbf{}\mathit{K}$).

n is the number of moles (1.70 mol).

The number of moles of the gas are,

$\mathit{M}\mathit{o}\mathit{l}\mathit{e}\mathit{s}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{Molar}\mathbf{}\mathbf{mass}}$

Determination of pressure

The number of moles will be,

$$\begin{gathered} \mathit{M}\mathit{o}\mathit{l}\mathit{e}\mathit{s}\mathbf{=}\frac{\mathbf{75}\mathbf{.}\mathbf{0}\mathbf{g}}{\mathbf{44}\mathbf{.}\mathbf{013}\mathbf{g}\mathbf{/}\mathbf{m}\mathbf{o}\mathbf{l}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{70}\mathit{m}\mathit{o}\mathit{l} \end{gathered}$$

And thepressure of the gasis,

$$\begin{gathered} \mathit{P}\mathbf{=}\frac{\mathbf{nRT}}{\mathbf{V}} \\ \mathit{P}\mathbf{=}\frac{\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{70}\mathbf{mol}\mathbf{)}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{0821}{\mathbf{LatmK}}^{\mathbf{-}\mathbf{1}}{\mathbf{mol}}^{\mathbf{-}\mathbf{1}}\mathbf{\times }\mathbf{388}\mathbf{}\mathbf{K}}{\mathbf{3}\mathbf{.}\mathbf{1}\mathbf{}\mathbf{L}} \\ \mathit{P}\mathbf{=}\mathbf{17}\mathbf{.}\mathbf{47}\mathbf{}\mathit{a}\mathit{t}\mathit{m} \end{gathered}$$

Thus, the pressure of the given gas is17.47 atm.