Question #5a3fa

2 Answers
Apr 10, 2017

Answer:

2000K
(non rounded: 1638K)

Explanation:

#(P_1V_1)/T_1=(P_2V_2)/T_2#

The conditions of STP for gases is 0˚ C and 1 atm

We need to convert our units for the equation written above to be applicable.

#P_1#-- 1 atm
#V_1#-- 0.03 Liters
#T_1#-- 273 Kelvin, 0˚C + 273= Kelvin

#P_2#-- 3 atm: 1 atm = 760 mmHg #(2280mmHg)/760= 3 atm#
#V_2#-- 0.06 Liters
#T_2#-- We will solve for this as a variable

#[.03xx 1]/273=[3 xx 0.06)/x# Now just finish this through simple algebra to get 1638 K

There is 1 significant digit in the rounded version (since 30 and 60 ml have 1 sig fig), Final Answer: 2000K

Apr 10, 2017

Answer:

Use the combined gas law for this question.

The final temperature will be#~~"2000 K"#.

Explanation:

There are three variables in this question, volume #(V)#, temperature #(T)#, and pressure #(P)#. These variables represent the combined gas law . The equation is:

#(P_1V_1)/T_1=(P_2V_2)/T_2#

where #P_1# is the initial pressure in kilopascals (kPa), #V_1# is the initial volume, #T_1# is the initial temperature in Kelvins, #P_2# is the final pressure in kPa, #V_2# is the final volume, and #T_2# is the final temperature in Kelvins.

As you can see, we will need to make some conversions of the units for the variables.

STP
STP is currently #0^@"C"#, or #"273.15 K"# for gas laws. Pressure is #"10^5 Pa"# or #"100 kPa"#. The pressure needs to be converted from #"mmHg"# to #"kPa"#.

List what is known/given:
#P_1="100 kPa"#
#V_1="30 mL"#
#T_1="273.15 K"#
#P_2=2280color(red)cancel(color(black)("mmHg"))xx(1 "kPa")/(7.50061561303color(red)cancel(color(black)("mmHg")))="303.9750492 kPa"#
#V_2="60 mL"#

List what is unknown: #T_2#

Solution
Rearrange the combined gas law to isolate #T_2#. Substitute the known values into the equation and solve.

#T_2=(P_2V_2T_1)/(P_1V_1)#

#T_2=(303.9750492color(red)cancel(color(black)("kPa"))xx60color(red)cancel(color(black)("mL"))xx273.15"K")/(100color(red)cancel(color(black)("kPa"))xx30color(red)cancel(color(black)("mL")))="2000 K"# rounded to one significant figure