Question

How many moles of gas are contained in 890.0 mL at 21${}^\circ C$ and 750.0mmHg pressure?

Answer 1

Hint: Number of moles of 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 which 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 a gas,
P = 750 mmHg = $\dfrac{750}{760}atm$,
V = 890 mL = 0.89 L,
T = 21${}^\circ C$ = 294.15 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
\[\dfrac{750}{760}\times 0.89=n\times 0.082\times 294.15 \\
n=\dfrac{750\times 0.89}{760\times 0.082\times 294.15} \\
n\cong 0.036 \\
\]
So, the number of moles of a gas contained in 890.0 mL at 21${}^\circ C$ and 750.0mmHg pressure is 0.036 moles.

Note: It is important to note that 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 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 gas constant will be
\[R=0.082\dfrac{L.atm}{K.mol}\]