How can I calculate the density of air?

Question

I major in chemical engineering, and I'm solving a example of unit operations. The textbook is Warren L. McCabe, Unit Operations of Chemical Engineering 7th ed. Here is example 24.1.

And this is its solution.

From this, it says that the density of air is 29/369 × 492/620. But it omitted the untis, so I can't understand the equation. I assume that this equation is probably ρ = PM/RT, since molecular weight of air is 28.97 g/mol when I searched for it. But the numbers 369, 492, 620 are still mystery. What is those?

Answer 1

If you look at Text equation 1.29, the 492/620 is Temperature in Rankine.

$$T°F = T°R - 459.67$$

Ice point is 491.67°R. 160°F = 619.67°R.

If you do the math, it does not equal 0.0641, because the 369 is wrong. The math to get 0.0641 means 369 should be 359.

1 lb-mole of an ideal gas at 0°C and 1 atm occupies 359 $ft^3$ absolute.

The molecular weight of air is 29 lb/lb-mole.

$$\frac {29 lb/lb-mole}{359 ft^3/lb-mole} \times \frac {492°R}{160°F + 460°R} = 0.0461 lb/ft^3$$