# Air has an average molar mass of 29.0 g/mol. Find the density of air at 0.97 atm and 30 degree C.

## Question:

Air has an average molar mass of {eq}29.0\ g/mol {/eq}. Find the density of air at {eq}0.97\ atm {/eq} and {eq}30 ^\circ C {/eq}.

## Molar Mass:

The molar mass of substances is a quantity that gives the mass of the substance per mole. One way to determine the molar mass of a substance is by summing the total mass of each element in the chemical formula. We can use the molar mass in order to determine the mass of the reagent we need to weigh for our experiments.

Determine the densityof air of the given pressure and temperature using the ideal gas equation, {eq}\displaystyle \frac{n}{V} = \frac{P}{RT} {/eq}, and then multiplying it by the given density of air. Thus, we need to solve for {eq}\displaystyle \rm{Molar\ mass} = \frac{n}{V}\cdot \rho = \frac{P}{RT}\cdot \rho {/eq}. We proceed with the solution.

{eq}\begin{align} \displaystyle \rm{Molar\ mass} &= \frac{n}{V}\cdot \rho\\ &= \frac{P}{RT}\cdot \rho\\ &= \frac{0.97\ atm}{ 0.08206\ \rm{L\ atm/mol\ K}\cdot (30+273\ K)}\cdot 29.0\rm{g/mol}\\ &= 1.13\ \rm{g/L}\\ \text{or}\\ &= 1.13\ \rm{g/L}\times \frac{1}{1000}\rm{L/mL}\\ &= 0.00113\ \rm{g/mL} \end{align} {/eq}