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

1 Answer
Mar 15, 2016

Answer:

#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#.