Question

Identify the correct relationship between pressure (P), density (d), molar mass (M) and Temperature (T) for an ideal gas from the following.

Options

• \[\mathrm{P}=\frac{\mathrm{d}\times\mathrm{M}\times\mathrm{R}}{\mathrm{T}}\]

• \[\mathrm{P}=\frac{\mathrm{d}\times\mathrm{R}\times\mathrm{T}}{\mathrm{M}}\]

• \[\mathrm{P}=\frac{\mathrm{M}\times\mathrm{R}\times\mathrm{T}}{\mathrm{d}}\]

• \[\mathrm{P}=\frac{\mathrm{d}\times\mathrm{M}\times\mathrm{T}}{\mathrm{R}}\]

Answer 1

\[\mathrm{P}=\frac{\mathrm{d}\times\mathrm{R}\times\mathrm{T}}{\mathrm{M}}\]

Explanation:

\[\mathrm{PV=nRT=\frac{m}{M}\times RT}\]
\[\therefore\quad\mathrm{P}=\frac{\mathrm{mRT}}{\mathrm{MV}}\]
\[\therefore\quad\mathrm{P}=\frac{\mathrm{dRT}}{\mathrm{M}}\quad....\left(\because\mathrm{d}=\frac{\mathrm{m}}{\mathrm{V}}\right)\]