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A certain quantity of real gas occupies a volume of 0.15 dm30.15~ \mathrm{dm}^{3}0.15 dm3 at 100 atm100 \mathrm{~atm}100 atm and 500 K500 \mathrm{~K}500 K when its compressibility factor is 1.07 . Its volume at 300 atm and 300 K300 \mathrm{~K}300 K (When its compressibility factor is 1.4 ) is ___________ ×10−4 dm3\times 10^{-4} ~\mathrm{dm}^{3}×10−4 dm3 (Nearest integer)
z=PVnRT ; n=PVZRT Z1=1.07, P1=100 atm, V1=0.15 L, T1=500 K Z2=1.4, P2=300 atm, T2=300 K, V2=? P1 V1Z1 RTI=P2 V2Z2 RT2=n V2=1.41.07 × .03 =392 × 10−4 dm3 \begin{aligned} & \mathrm{z}=\frac{\mathrm{PV}}{\mathrm{nRT}} ; \mathrm{n}=\frac{\mathrm{PV}}{\mathrm{ZRT}} \\\\ & \mathrm{Z}_1=1.07, \mathrm{P}_1=100 \mathrm{~atm}, \mathrm{~V}_1=0.15 \mathrm{~L}, \mathrm{~T}_1=500 \mathrm{~K} \\\\ & \mathrm{Z}_2=1.4, \mathrm{P}_2=300 \mathrm{~atm}, \mathrm{~T}_2=300 \mathrm{~K}, \mathrm{~V}_2=? \\ & \frac{\mathrm{P}_1 \mathrm{~V}_1}{\mathrm{Z}_1 \mathrm{RT}_{\mathrm{I}}}=\frac{\mathrm{P}_2 \mathrm{~V}_2}{\mathrm{Z}_2 \mathrm{RT}_2}=\mathrm{n} \\ & \mathrm{V}_2=\frac{1.4}{1.07} \times .03 \\\\ &=392 \times 10^{-4} \mathrm{dm}^3 \end{aligned} z=nRTPV ; n=ZRTPV Z1=1.07, P1=100 atm, V1=0.15 L, T1=500 K Z2=1.4, P2=300 atm, T2=300 K, V2=? Z1 RTIP1 V1=Z2 RT2P2 V2=n V2=1.071.4 × .03 =392 × 10−4 dm3
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