Van der Waal's Equation

Q. Consider the van der Waals constants, a and b, for the following gases.
$\begin{array}{ccccc}\text{Gas}& \text{Ar}& \text{Ne}& \text{Kr}& \text{Xe}\\ \text{a (atm}d{m}^{6}mo{l}^{-2})& 1.3& 0.2& 5.1& 4.1\\ b\left({10}^{-2}d{m}^{3}mo{l}^{-1}\right)& 3.2& 1.7& 1.0& 5.0\end{array}$
Which gas is expected to have the highest critical temperature?

1. Xe
2. Ne
3. Kr
4. Ar

Q. At low pressure, if $RT=2\sqrt{a.P}$, then the volume occupied by a real gas is (where $a$ is the van der Waal's gas constant for pressure correction)

1. $\frac{2RT}{P}$
2. $\frac{2P}{RT}$
3. $\frac{RT}{2P}$
4. $\frac{2RT}{P}$

Q. In certain low pressure region for $1\text{mol}$ of real gas curve of $Zv/s\frac{1}{v}$ is plotted at constant temperature as follows -



then temperature (T) of above mentioned real gas is -
$[\text{Given}:a=5.5{\text{atm L}}^2{\text{mol}}^{-2},R=0.08\text{atm L}{\text{mol}}^{-1}{\text{K}}^{-1}$]

1. $230.4\text{K}$
2. $312.5\text{K}$
3. $273.15\text{K}$
4. $300\text{K}$

Q. For one mole of a Van der Waals gas when $b=0$ and $T=300K$, the $PVvs.1/V$ plot is shown below. The value of the Van der Waals constant $a\left(atm{L}^{2}mo{l}^{-2}\right):$

Q. A real gas obeying van der Waals equation will resemble ideal gas if:

1. Constants a and b are negligibly small
2. a is small and b is large
3. a is large and b is small
4. Both a and b are large

Q. For one mole of a Van der Waals gas when $b=0$ and $T=300K$, the $PVvs.1/V$ plot is shown below. The value of the Van der Waals constant $a\left(atm{L}^{2}mo{l}^{-2}\right):$

1. $1.0$
2. $4.5$
3. $1.5$
4. $3.0$

Q. For reactions $P\to Q$ and $X\to Y$ Arrhenius constants are ${10}^6$ and ${10}^8$ respectively. If $E_{P\to Q}=1500\text{cal/mole}$ and $E_{x\to y}=2000\text{cal/mole}$ then find the temperature at which their rate constants are same. (Given $R=2\text{cal/mole.K}$)

Q. At high temperature and low pressure, the van der Waals equation is reduced to:

1. $(P+\frac{a}{V^2})V=RT$
2. $PV=RT$
3. $P(V-b)=RT$
4. $(P+\frac{a}{V^2})(V-b)=RT$

Q. Choose the correct statement regarding the van der waals' equation when one mole of a has is kept at high temperature and low pressure:

1. $(P+\frac{a}{V^2})V=RT$
2. $PV=RT$
3. $P(V-b)=RT$
4. $(P+\frac{a}{V^2})(V-b)=RT$

Q. For one mole of a van der waal's gas when $b=0andT=300K,thePVvs,1/Vplot$. The value of the van der waal's constant ${}^{\prime }{a}^{\prime }(atm.litr{e}^{2}mo{l}^{-2})$ is

1. $3.0$
2. $1.5$
3. $4.5$
4. $1.0$

Q. Milliequivalents of $Se{O}_3^{2-}$ is :

1. $\frac{55}{72}$
2. $\frac{55}{36}$
3. $\frac{11}{36}$
4. $\frac{11}{6}$

Q.

If a real gas is following equation $P(V-nb)=nRT$, at low pressure then find the intercept and slope of graph between $\frac{d}{p}v/sP$.

1. $\frac{MR}{T},\frac{M(RT{)}^2}{b}$
2. $\frac{M}{RT},-\frac{Mb}{(RT{)}^2}$
3. $\frac{RT}{M},-\frac{b}{M(RT{)}^2}$
4. $\frac{Mb}{RT},-\frac{M}{(RT{)}^2}$

Q. For one mole of a van der Waal's gas when $b=0$ and $T=300K$, the $PV$ vs. $1/V$ plot is shown below. The value of the van der Waals' constant $a$ (atm. $litr{e}^{2}mo{l}^{-2})$ is

1. $4.5$
2. $1.0$
3. $1.5$
4. $3.0$