Ideal gas law problem check?

If I have 4.1 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature?
I want to check that I completed this problem right before continuing with the rest of my problems to ensure I'm doing them correctly. Thanks!

2 Answers
Apr 25, 2018

The temperature is #2.0xx10^2# #"K"#.

Explanation:

Equation for the ideal gas law:

#PV=nRT#,

where:

#P# is pressure, #V# is volume, #n# is moles, #R# is the gas constant (varies with units for pressure), and #T# is temperature in Kelvins.

Known

#P="5.6 atm"#

#V="12 L"#

#n="4.1 moles"#

#R="0.082056 L atm K"^(-1) "mol"^(-1)"#

Unknown

#T#

Solution

Rearrange the equation to isolate #T#. Plug in the known values and solve.

#T=(PV)/(nR)#

#T=(5.6color(red)cancel(color(black)("atm"))xx12color(red)cancel(color(black)("L")))/(4.1color(red)cancel(color(black)("mol"))xx0.082056 color(red)cancel(color(black)("L")) color(red)cancel(color(black)("atm")) "K"^(-1) color(red)cancel(color(black)("mol"))^(-1))=2.0xx10^2# #"K"# (rounded to two significant figures)

Apr 25, 2018

#T = 199.73 K#

Explanation:

Use the formula

#PV = nRT#

re-arranging for temperature:

#T =( PV)/(nR)#

Plug-in values:

Remember R is a constant = #0.08206 (L*atm)/(mol *K)#

#T = ((5.6 atm)(12 L)) / ((4.1 mol) (0.08206 (L*atm)/(mol *K))#

cancel units and solve:

#T = 199.73 K #