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

Question

Caleb Adams · Accepted Answer

#318kPa#

Remember that, under the assumption that the gas's volume and number of moles stay constant, Gay-Lussac's Law states that pressure and temperature are directly correlated.

The following formula can be used to mathematically express Gay-Lussac's Law:

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

where P_1 denotes the initial pressure, T_1 the initial temperature (Kelvin), P_2 the final pressure, and T_2 the 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#.

Cameron Andrews · Answer

undefined The new pressure would depend on the initial pressure of the closed food jar at STP and the temperature change. You can use the combined gas law equation to calculate the new pressure.