A closed food jar has a fixed volume at STP. What would the new pressure be at 45°C?
1 Answer
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
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)#
#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)))#
#color(teal)(P_2)=(color(magenta)(318.15K))(color(orange)(101.325kPa)/color(purple)(273.15K))#
#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)|)))#