What is the temperature in Celsius inside a sealed 10.0 L flask which contains 14.2 g of nitrogen gas at 2.0 atm?
1 Answer
Explanation:
Your strategy here will be to
- use the ideal gas law equation to find the temperature of the gas in Kelvin
- use the known conversion factor to go from Kelvin to degrees Celsius
The ideal gas law equation looks like this
#color(blue)(PV = nRT)" "# , where
Notice that the problem does not provide you with the number of moles of gas, but that it does give you the mass of the sample.
To get the number of moles that are present in that
#14.2 color(red)(cancel(color(black)("g"))) * "1 mole N"_2/(28.0134color(red)(cancel(color(black)("g")))) = "0.5069 moles N"_2#
Rearrange the ideal gas law equation and solve for
#PV = nRT implies T = (PV)/(nR)#
This will give you
#T = (2.0 color(red)(cancel(color(black)("atm"))) * 10.0color(red)(cancel(color(black)("L"))))/(0.5069color(red)(cancel(color(black)("moles"))) * 0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * "K")) = "480.6 K"#
Now, the following relationship exists between temperature expressed in degrees Celsius and temperature expressed in Kelvin
#color(blue)([""^@"C"] = ["K"] - 273.15)#
In your case, the temperature of the gas in degrees Celsius will be
#t = 480.6 - 273.15 = 207.45^@"C"#
Rounded to two sig figs, the number of sig figs you have for the pressure of the gas, the answer will be
#t = color(green)(210^@"C")#