Question

How do you calculate the volume occupied by 64.0 grams $C{{H}_{4}}$ at $127{}^\circ C$ a pressure of 1535 torr?

Answer 1

Hint:The volume occupied by gas can be calculated using the ideal gas law equation. The ideal gas law equation gives the relation between the pressure exerted by the gas, the volume occupied by the gas, the temperature of the gas, the gas constant, and the number of moles of the gas.

Complete step-by-step answer:We know that an ideal gas is a gas in which
- the molecules either attract or repel each other
- the molecules do not occupy any space themselves.
The concept of an ideal gas is hypothetical as no gas can follow the above rules completely. Nevertheless, there are a few gases that do come close to the ideal gas behavior.
The ideal gas law equation is given by
PV=nRT
Where P is the pressure exerted by the gas,
V is the volume occupied by the gas,
n is the number of moles of the gas,
R is the gas constant,
And T is the temperature of the gas.

Now, it is given to us that for gas,
P = 1535 torr = $\dfrac{1535}{760}atm$,
$n=\dfrac{64\text{ }g}{16\text{ }g/mol}=4\text{ }mol$,
T = 127${}^\circ C$ = 400 K,
And the gas constant $R=0.082\text{ }L\text{ }atm\text{ }{{K}^{-1}}mo{{l}^{-1}}$.
Substituting these values in the gas law equation, we get
\[
\dfrac{1535}{760}\times V=4\times 0.082\times 400 \\
V=\dfrac{4\times 0.082\times 400\times 760}{1535} \\
V\cong 64.96\text{ }L \\
\]
So, the volume occupied by 64.0 grams of $C{{H}_{4}}$ at $127{}^\circ C$ under a pressure of 1535 torr is approximately 64.96 L.

Note:It is important to note that the right units are used while using the ideal gas law equation.
The temperature must always be in kelvin K.
When the unit of pressure is in Pa, and the unit of volume is ${{m}^{3}}$, the value of the gas constant will be
\[R=8.31\dfrac{J}{K.mol}\]
When the unit of pressure is in atm, and the unit of volume is L, the value of the gas constant will be
\[R=0.082\dfrac{L.atm}{K.mol}\]