Question

45 points


Detailed Answer needed


$\textbf{\underline\underline{Question}}}$


A gas cylinder is filled with helium at 2000 mm.Due to leakage, the pressure dropped to 1500 mm in 40 min.When the same cylinder is filled with another gas at the same pressure, the pressure dropped from 2000mm to 1500 mm in 200 min .What is the molecular weight of the gas ?​

Answer 1

Explanation:

before solving the question we need to know equation/formula like

1) ideal gas equation - PV=nRT         where n is the number of moles

2)rate of diffusion = moles diffused per unit time = n/t

3) rate ∝1/√M.Wt              M.Wt =molecular weight

solution : since it is a gas cylinder,its volume will be constant ,and R is universal gas constant ,also nothing mentioned about temp so it can also be taken constant

Therefore                            P∝n                (moles present or left in container )

so change in pressure can be taken equal to change in number of moles to make question easier ΔP =kΔn (where k is some constant of proportionality)

                                  or Δn =ΔP/k

now rate of diffusion in first case =Δn₁/t₁=ΔP₁/kt₁

                                                       =(2000-1500) mm of hg/k40 min

                                                        =500mm of hg/k40min..........1

rate of diffusion in second  case =Δn₂/t₂=ΔP2/kt2                                                        =(2000-1500 )mm of hg/k200 min

                                                        =500 mm of hg /k200 min..................2

by dividing 1 and 2

(rate)₁/(rate )₂=5

also (rate)₁/(rate )₂=√M.wt2/√M.wt1

               5=√M.wt₂/√4

           √M.wt₂ =10

           M.wt ₂ =100

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Answer 2

✨✨HEY MATE HERE IS YOUR ANSWER:-✨✨
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FULL EXPLANATION:-

Before solving the question we need to know equation/formula like

1) ideal gas equation - PV=nRT         where n is the number of moles

2)rate of diffusion = moles diffused per unit time = n/t

3) rate ∝1/√M.Wt              M.Wt =molecular weight

solution : since it is a gas cylinder,its volume will be constant ,and R is universal gas constant ,also nothing mentioned about temp so it can also be taken constant

Therefore                            P∝n                (moles present or left in container )

so change in pressure can be taken equal to change in number of moles to make question easier ΔP =kΔn (where k is some constant of proportionality)

                                  or Δn =ΔP/k

now rate of diffusion in first case =Δn₁/t₁=ΔP₁/kt₁

                                                       =(2000-1500) mm of hg/k40 min

                                                        =500mm of hg/k40min..........1

rate of diffusion in second  case =Δn₂/t₂=ΔP2/kt2                                                        =(2000-1500 )mm of hg/k200 min

                                                        =500 mm of hg /k200 min..................2

by dividing 1 and 2

(rate)₁/(rate )₂=5

also (rate)₁/(rate )₂=√M.wt2/√M.wt1

               5=√M.wt₂/√4

           √M.wt₂ =10

           M.wt ₂ =100

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