Question

A closed food jar has a fixed volume at STP. What would the new pressure be at 45°C?

Answer 1

`318kPa`

Explanation:

Recall that Gay-Lussac's Law states that pressure is directly proportional to temperature , as long as the volume and number of moles of the gas remain constant.

Gay-Lussac's Law can be expressed mathematically with the formula,

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

where:
`P_1=`initial pressure
`T_1=`inital temperature (Kelvin)
`P_2=`final pressure
`T_2=`final temperature (Kelvin)

Determining the Final Pressure
`1`. Start by determining the values for each variable in the formula.

STP conditions (initial):
initial pressure `color(orange)((P_1))`: `color(orange)(101.325kPa)`
initial temperature `color(purple)((T_1))`: `color(purple)(273.15K)`

New conditions (final)
final pressure `color(teal)((P_2))`: `color(teal)(P_2)`
final temperature `color(magenta)((T_2))`: `45^@C+273.15=color(magenta)(318.15K)`

`2`. Rearrange Gay-Lussac's formula in terms of `color(teal)(P_2)`.

`color(orange)(P_1)/color(purple)(T_1)=color(teal)(P_2)/color(magenta)(T_2)`

`color(teal)(P_2)=(color(magenta)(T_2))((color(orange)(P_1))/(color(purple)(T_1)))`

`3`. Using these values, substitute them into the rearranged formula.

`color(teal)(P_2)=(color(magenta)(318.15K))(color(orange)(101.325kPa)/color(purple)(273.15K))`

`4`. Solve for `color(teal)(P_2)`.

`color(teal)(P_2)=(color(magenta)(318.15color(red)cancelcolor(magenta)K))(color(orange)(101.325kPa)/color(purple)(273.15color(red)cancelcolor(purple)K))`

`color(teal)(P_2)=118.0177512kPa`

`color(teal)(P_2)~~color(green)(|bar(ul(color(white)(a/a)318kPacolor(white)(a/a)|)))`

`:.`, the final pressure is `318kPa`.