Single Choice

If volume occupied by $$CO_{2}$$ molecules is negligible, then what will be the pressure $$\left (\dfrac {P}{5.277}\right )$$ exerted by one mole of $$CO_{2}$$ gas at $$300\ K? (a = 3.592\ atm\ L^{2} mol^{-2})$$.

A$$7$$
B$$8$$
Correct Answer
C$$9$$
D$$3$$

Solution

$$\left (P + \dfrac {an^{2}}{V^{2}}\right )(V - nb) = nRT$$
$$\left (P + \dfrac {a}{V^{2}}\right )(V - b) = RT (\because n = 1)$$
If $$b$$ is negligible
$$P = \dfrac {RT}{V} - \dfrac {a}{V^{2}}$$
The equation is quadratic in $$V$$, thus
$$V = \dfrac {+RT \pm \sqrt {R^{2}T^{2} - 4aP}}{2P}$$
Since $$V$$ has one value at given $$P$$ and $$T$$, thus numerical value of discriminant $$= 0$$
$$R^{2}T^{2} = 4aP$$
$$P = \dfrac {R^{2}T^{2}}{4a} = \dfrac {(0.0821)^{2}(300)^{2}}{4\times 3.592} \therefore \dfrac {P}{5.277} = 8$$.

SIMILAR QUESTIONS

States of Matter - Gas and Liquid

Which of the following expressions correctly represents the van der Waals equation of state?

States of Matter - Gas and Liquid

The term that corrects for the attractive forces present in a real gas in the Vander Waals' equation is:

States of Matter - Gas and Liquid

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

States of Matter - Gas and Liquid

A certain gas $$A$$ polymerizes to a small extent at a given temperature and pressure, $$nA \rightleftharpoons A_{n}$$. Show that the gas obeys the approx. equation $$\dfrac {PV}{RT} = \left [1 - \dfrac {(n - 1)K_{C}}{V^{n - 1}}\right ]$$ where $$K_{C} = \dfrac {[A_{n}]}{[A]^{n}}$$ and $$V$$ is the volume of the container. Assume that initially one mole of $$A$$ was taken in the container.

States of Matter - Gas and Liquid

Calculate the volume occupied by $$0.2$$ mole of a Vander Waal gas at $$27^o$$C and $$0.0821$$ atm. $$[a=4.105L^2$$ atm $$mol^{-2}, b=\dfrac{1}{6}L mol^{-1}]$$.

States of Matter - Gas and Liquid

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is:

States of Matter - Gas and Liquid

In van der Waals equation for a non-ideal gas, the term that accounts for intermolecular force is :

States of Matter - Gas and Liquid

What is the pressure of $$2$$ mole of $$NH_3$$ at $$27^oC$$ when its volume is $$5$$ litre in vander Waal's equation $$?(a = 4.17, b = 0.03711)$$

States of Matter - Gas and Liquid

Which of the following statements are false? Rewrite the false statement correctly. In the van der Waal's equation, $$\Bigg(P+\dfrac{n^2 a}{V^2}\Bigg)(V-nb)=n RT$$ the constant 'a' represents the actual volume of the gas molecules.

States of Matter - Gas and Liquid

When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P-V curve, V-T curve,P-T curve etc. For example, P-V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V-T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed. Now, answer the questions : Two Vander Waals gases have same value 'b' but different 'a' value thwn which of the following statement is correct under similar condition .

Contact Details