A sample of gas at #"31"^@"C"# has a pressure of #"745 Torr"#. What is the pressure if the temperature is increased to #"78"^@"C"#?

2 Answers
Apr 9, 2017

Answer:

The final pressure will be #"860. torr"#.

Explanation:

This is an example of Gay-Lussac's law , which states that the pressure of a gas with a constant volume and amount, is directly proportional to the temperature in Kelvins. This means that if the pressure is increased, the temperature will increase, and vice-versa.

The equation that is used for this law is:

#P_1/T_1=P_2/T_2#

where #P_1# is the initial pressure, #P_2# is the final pressure, #T_1# is the initial temperature, #T_2# is the final temperature.

Write what is known.
#P_1="745 torr"#
#T_1="31"^@"C" + 273.15=304 "K"#
#T_2="78"^@"C" + 273.15=351 "K"#

Write what is unknown: #P_2#

Solution
Rearrange the equation to isolate #P_2#. Substitute the known values into the equation and solve.

#P_2=(P_1T_2)/T_1#

#P_2=(745"torr"xx351color(red)cancel(color(black)("K")))/(304color(red)cancel(color(black)("K")))="860. torr"# (rounded to three significant figures)

Apr 9, 2017

Answer:

#P_2 = 860# torr

Explanation:

With a constant container volume, Charles' Law becomes simply:
#P_1/T_1 = P_2/T_2#
Rearrange for your known values:

#P_2 = P_1 * T_2/T_1# ; #P_2 = 745 * 351/304# ; #P_2 = 860# torr

The ideal gas law (Charles' Law) states:
#(P_1 * V_1)/T_1 = (P_2 * V_2)/T_2#
Where #P_1,_2# are pressures – units don't matter in this case as long as they are consistent, because this is a ratio.
#V_1,_2# are the corresponding volumes in Liters
#T_1,_2# are the temperatures in degrees Kelvin