A sample of a gas has a pressure of #"0.370 atm"# at a temperature of #"5.00"^@"C"#. What will the pressure be if the temperature is lowered to #"0"^@"C"#?

1 Answer
May 12, 2017

Answer:

The pressure at #"273.15 K"# #(0^@"C")# will be #"0.363 atm"#.

Explanation:

Gay-Lussac's gas law will be used to solve this problem. It states that the pressure of a gas is directly proportional to its Kelvin temperature, as long as mass and volume are held constant. This means that if the volume increases, so does the temperature and vice-versa. The equation for this law is:

#P_1/T_1=P_2/T_2#

The given data has temperature in degrees Celsius, so it needs to be converted to Kelvins. This is done by adding #"273.15"# to the Celsius temperature.

Organize your data:

Given

#P_1="0.370 atm"#

#T_1="5.00"^@"C" + 273.15="278.15 K"#

#T_2="0.00"^@"C + 273.15 ="273.15 K"#

Unknown:

#P_2#

Solution
Rearrange the equation to isolate #P_2#. Insert the given data and solve.

#P_2=(P_1T_2)/(T_1)#

#P_2=(0.370color(white)(.)"atm"xx273.15color(red)cancel(color(black)("K")))/(278.15color(red)cancel(color(black)("K")))="0.363 atm"# (rounded to three significant figures)