# 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

*number of moles* of gas

**always** expressed in *Kelvin*!

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 **molar mass**.

#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 **match** those used for the universal gas constant!

#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")#