The density of air at ordinary atmospheric pressure and 25.0 degrees Celsius is 1.19 g/L. What is the mass in megagrams (Mg) of the air in a room...

Tuesday, July 25, 2017

The density of air at ordinary atmospheric pressure and 25.0 degrees Celsius is 1.19 g/L. What is the mass in megagrams (Mg) of the air in a room...

Hello!

I suppose that air in a room has the same pressure and temperature, and therefore has the given density. Because by definition density is mass divided by volume, we have $\displaystyle{m}=\rho\cdot{V},$ where $\displaystyle\rho$ is the density (it is given) and $\displaystyle{V}$ is the volume of a room.

We have to compute the volume of a room and take into account different units of measure (liters, megagrams, feet). The volume is width*length*height, but remember they...

Hello!

We have to compute the volume of a room and take into account different units of measure (liters, megagrams, feet). The volume is width*length*height, but remember they are given in feet. One liter is 10cm*10cm*10cm, one foot is 30.48cm which is 3.048 times greater than 10 cm.

This way, the volume in liters is $\displaystyle{12.50}\cdot{17.25}\cdot{9.00}\cdot{{\left({3.048}\right)}}^{{3}},$ and the mass in grams is $\displaystyle{1.19}\cdot{12.50}\cdot{17.25}\cdot{9.00}\cdot{{\left({3.048}\right)}}^{{3}},$ which is approximately $\displaystyle{65393}{\left({g}\right)}$ (about 65kg). In megagrams, millions of grams, it will be million times less, i.e. $\displaystyle{0.065393}{M}{g{.}}\approx{6.5}\cdot{{10}}^{{-{2}}}{M}{g{.}}$