Question

A sample of pure nitrogen gas is at 27 degrees C and 380 mm Hg occupied a volume of 492 mL.
a. using the ideal gas law, determine the number of moles of gas in this sample?
b. calculate the mass of the gas sample

Answer 1

a) \[P \times V = n \times R \times T\]
\[n= \frac{ P \times V }{ R \times T }\]

convert your pressure value from mmHg to atm with the conversion factor "1atm/760 mmHg)
convert the temperature to K "K=C+273.15"
convert the volume from mL to L (1L/1000mL)
R= 0.082 atm L/mol K

b) with the number of moles calculated from a) multiply by the MM of N2 (14 x 2) to get the mass of N2

Answer 2

thank you so much! the only question i have is on my paper it says R is gas constant (8.31 J/mol-K) and your saying its 0.082 atm L/mol K. which one should i use?

Answer 3

@Cuanchi

Answer 4

n must be in moles so what units must R be in?
Write your units into your equation and you will see which units cancel out.

Answer 5

Yes!
R= constant of the gases can have many different values depending on the units.

It is like said the length of a book is 11 inches or said is 27.94 cm.

For the general gas Law the most simple way to remember the R value is 0.082 atm L/mol K, because the other values in the formula are in the same units.
Then for example if you want to express the R in place of atmospheres in mmHg, the value is going to be 0.082 x 760 = R= 62.32 mmHg L/mol K.

In your case the 8.314 J is equivalent to 0.082 atm L/mol K. But the units in this case is Joule/mol K ; Joule = kg m^2/s^2= N x m = Pa x m^3. Atmospheres is unit of pressure, pressure is equal to force/area, force is mass times acceleration, acceleration is velocity over time. They are all derivative units. This form of R is mostly used in calculations of energy, since joules is a energy unit.
You can check in Wikipedia they have a extensive list of values of R in different units
http://en.wikipedia.org/wiki/Gas_constant

Answer 6

If you still want to use the R in J/mol K, you will have to convert the pressure to Pa=pascals (1 atmosphere =101 325 pascals) and the volume to m^3 (1m^3=1000L)