Question

If the volume is 500 mL, the mass of air is 60g (molar mass of air= 29g/mol), and the temperature is 0 C, what is the pressure inside the bottle?

Answer 1

The pressure inside the bottle is 92.678 atm.

Step-by-step explanation:

An ideal gas is characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). The relationship between them constitutes the ideal gas law, an equation that relates the three variables if the amount of substance, number of moles n, remains constant and where R is the molar constant of the gases:

P * V = n * R * T

In this case:

• P= ?
• V= 500 mL= 0.500 L
• n= 60 g*
  `(1 mole)/(29 g)` = 2.07 moles
• R= 0.082
  `(atm*L)/(mol*K)`
• T= 0 C= 273 K

Replacing:

P* 0.500 L= 2.07 moles* 0.082
`(atm*L)/(mol*K)` * 273 K

Solving:

`P=(2.07 moles* 0.082 (atm*L)/(mol*K) * 273 K)/(0.500 L)`

P= 92.678 atm

The pressure inside the bottle is 92.678 atm.