NEET Test Series from KOTA - 10 Papers In MS WORD
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CHXI06:STATES OF MATTER
314093
The van der Waals constants of gas A are given as \({\mathrm{\mathrm{a}\left(\mathrm{atm} \,\mathrm{L}^{2} \mathrm{~mol}^{-2}\right)=10}}\) \({\mathrm{\mathrm{b}\left(\mathrm{L} \,\mathrm{mol}^{-1}\right)=0.027}}\) The critical temperature of A is ____ K.
314094
If \(\mathrm{Z}\) is a compressibility factor, van der Waal's equation at low pressure can be written as
1 \(\mathrm{Z=1+\dfrac{R T}{p b}}\)
2 \(\mathrm{Z=1-\dfrac{a}{V R T}}\)
3 \(\mathrm{Z=1-\dfrac{p b}{R T}}\)
4 \(\mathrm{Z=1+\dfrac{p b}{R T}}\)
Explanation:
van der Waal's equation is given by \(\mathrm{\left(P+\dfrac{a}{V^{2}}\right)(V-b)=R T}\) At low pressure, \(\mathrm{\mathrm{V}}\) decreases. Thus, \(\mathrm{\dfrac{a}{V^{2}}}\) increases. However, \(\mathrm{\mathrm{V}}\) is still large enough in comparison to \(\mathrm{b}\), hence, \(\mathrm{b}\) can be neglected. Thus, van der Waal's equation becomes \(\mathrm{\left(P+\dfrac{a}{V^{2}}\right) V=R T}\) \(\mathrm{\Rightarrow P V+\dfrac{a}{V}=R T}\) \(\mathrm{\Rightarrow P V=R T-\dfrac{a}{V}}\) \(\mathrm{\Rightarrow \dfrac{P V}{R T}=1-\dfrac{a}{R T V}}\) \(\mathrm{Z=1-\dfrac{a}{R T V}\left[\because \dfrac{P V}{R T}=Z\right]}\)
314093
The van der Waals constants of gas A are given as \({\mathrm{\mathrm{a}\left(\mathrm{atm} \,\mathrm{L}^{2} \mathrm{~mol}^{-2}\right)=10}}\) \({\mathrm{\mathrm{b}\left(\mathrm{L} \,\mathrm{mol}^{-1}\right)=0.027}}\) The critical temperature of A is ____ K.
314094
If \(\mathrm{Z}\) is a compressibility factor, van der Waal's equation at low pressure can be written as
1 \(\mathrm{Z=1+\dfrac{R T}{p b}}\)
2 \(\mathrm{Z=1-\dfrac{a}{V R T}}\)
3 \(\mathrm{Z=1-\dfrac{p b}{R T}}\)
4 \(\mathrm{Z=1+\dfrac{p b}{R T}}\)
Explanation:
van der Waal's equation is given by \(\mathrm{\left(P+\dfrac{a}{V^{2}}\right)(V-b)=R T}\) At low pressure, \(\mathrm{\mathrm{V}}\) decreases. Thus, \(\mathrm{\dfrac{a}{V^{2}}}\) increases. However, \(\mathrm{\mathrm{V}}\) is still large enough in comparison to \(\mathrm{b}\), hence, \(\mathrm{b}\) can be neglected. Thus, van der Waal's equation becomes \(\mathrm{\left(P+\dfrac{a}{V^{2}}\right) V=R T}\) \(\mathrm{\Rightarrow P V+\dfrac{a}{V}=R T}\) \(\mathrm{\Rightarrow P V=R T-\dfrac{a}{V}}\) \(\mathrm{\Rightarrow \dfrac{P V}{R T}=1-\dfrac{a}{R T V}}\) \(\mathrm{Z=1-\dfrac{a}{R T V}\left[\because \dfrac{P V}{R T}=Z\right]}\)