Question

If you are given an ideal gas with pressure (p)259,392.00 pa and temperature (T)=200°c of 1 mole Argon gas in a volume 8.8dm3,calculate R to the correct number of significant figure and units under given conditions

Answer 1

Answer: $R=4.82436 \frac{Pa. m^{3}}{mol. K}$

Explanation:

The Ideal Gas equation is:  

$P.V=n.R.T$  (1)

Where:  

$P$ is the pressure of the gas  

$n$ the number of moles of gas  

$R=8.3144598 \frac{Pa. m^{3}}{mol. K}$ is the gas constant  

$T$ is the absolute temperature of the gas in Kelvin.

$V$ is the volume

It is important to note that the behavior of a real gas is far from that of an ideal gas, taking into account that an ideal gas is a single hypothetical gas. However, under specific conditions of standard temperature and pressure (T=0\°C=273.15 K and P=1 atm=101,3 kPa) one mole of real gas (especially in noble gases such as Argon) will behave like an ideal gas and the constant R will be $8.3144598 \frac{Pa. m^{3}}{mol. K}$.

However, in this case we are not working with standard temperature and pressure, therefore, even if we are working with Argon, the value of R will be far from the constant of the ideal gases.

Having this clarified, let's isolate $R$ from (1):

$R=\frac{PV}{nT}$  (2)

Where:

$P=259392 Pa$

$n=1 mole$

$T=200\°C=473.15 K$ is the absolute temperature of the gas in Kelvin.

$V=8.8 dm^{3}=0.0088 m^{3}$

$R=\frac{(259392 Pa)(0.0088 m^{3})}{(1 mole)(473.15 K)}$  (3)

Finally:

$R=4.82436 \frac{Pa. m^{3}}{mol. K}$