Question

A sample of 0.010 mole of oxygen gas is confined at 127°C and 0.80 atmosphere. What would be the pressure of this sample at 27 degrees C and the same volume?

Answer 1

The pressure will be 0.60 atm.

Since the volume is constant but the pressure and temperature are changing, this is an example of Gay-Lussac's Law:

`color(blue)(bar(ul(|color(white)(a/a)P_1/T_1=P_2/T_2color(white)(a/a)|)))" "`

Your data are:

`P_1 = "0.80 atm"`; `T_1 = "(127 + 273.15) K" = "400.15 K"`
`P_2 = "?"`; `color(white)(mmmm)T_2 = color(white)(l)"(27 + 273.15 K)" = "300.15 K"`

We can rearrange the above formula to get

`P_2=P_1 × T_2/T_1`

`P_2 = "0.80 atm" × (300.15 color(red)(cancel(color(black)("K"))))/(400.15 color(red)(cancel(color(black)("K")))) = "0.60 atm"`

The new pressure is 0.60 atm.