Consider a mole of a monoatomic gas which occupies a volume of 100c.c . at 36mm pressure. If the volume occupied by 5 moles of gas at one-third of the initial pressure and at a one-ninth of the initial temperature will be (V/3)mL . Find V. (approximate to two decimals).

Question

Consider a mole of a monoatomic gas which occupies a volume of 100c.c . at 36mm pressure. If the volume occupied by 5 moles of gas at one-third of the initial pressure and at a one-ninth of the initial temperature will be (V/3)mL . Find V. (approximate to two decimals). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Equation of state is given by, PV=nRT ∴ (P V/n T)= constant ∴ (P1 V1/n1 T1)=(P2 V2/n2 T2) ∴ (36 × 100/1 × T1)=(12 V2 × 9/5 × T1) ∴ V2=(36 × 100 × 5/12 × 9)=(500/3)c.c. 1c.c.=1mL

Q. Consider a mole of a monoatomic gas which occupies a volume of 100c.c . at 36mm pressure. If the volume occupied by 5 moles of gas at one-third of the initial pressure and at a one-ninth of the initial temperature will be 3V​mL . Find V. (approximate to two decimals).

Equation of state is given by, PV=nRT ∴nTPV​= constant ∴n1​T1​P1​V1​​=n2​T2​P2​V2​​ ∴1×T1​36×100​=5×T1​12V2​×9​ ∴V2​=12×936×100×5​=3500​c.c. 1c.c.=1mL

Q. Consider a mole of a monoatomic gas which occupies a volume of $100 c . c$ . at $36 mm$ pressure. If the volume occupied by $5$ moles of gas at one-third of the initial pressure and at a one-ninth of the initial temperature will be $\frac{V}{3} m L$ . Find $V .$ (approximate to two decimals).