Pressure of $$1$$ gm an ideal gas A at $$27$$°C is found to be $$2$$ bar. When $$2$$ g of another ideal gas B is introduced in the same flask at same temperature, the pressure becomes $$3$$ bar. Find a relationship between their molecular masses.

Question

Pressure  of $$1$$ gm an ideal gas A at $$27$$°C is found to be $$2$$ bar. When $$2$$ g of another ideal gas B is introduced in the same flask at same temperature, the pressure becomes $$3$$ bar. Find a relationship between their molecular masses.

Infinity Learn · Accepted Answer

pV $$=$$ nRTFor A gas, $$pAV=nART$$     ...(i)Similarly$$ for B gas, $$pBV=nBRT$$    $$-----(ii)Number$$ of moles of A gas ;$$nA=1MAMA=$$ molar mass of gasA Number of moles of B gas; $$nB=2MBMB=$$ molar mass of gas BPressure of gas A, $$pA=2$$ bar Total pressure, ptotal $$=pA+pB=3$$ bar Pressure of gas B, $$pB=ptotal$$ $$-pA=3-2=1barV$$ , R and T are same for both the gases.Hence, from Eqs.$$(i) and (ii), we get $$pApB=nAnB=1$$×MBMA×$$2MBMA=2pApB=2$$×$$21MB=4MAAlternate$$ $$method(b)$$ (i) ∵$$pT=pA+pBGiven$$, $$pT=3$$ bar and $$pA=2$$ bar ∴ $$pB=3-2=1bar$$ (ii) ∵$$pV=nRT=wMRT$$∴ For (A)2=1MA---------(I)∵$$pA=2$$ bar and V,T are constant. $$wA=1$$ g,$$MA=$$ molar mass of ASimilarly for (B)1=2MB$$ $$--------(ii)∵$$pB=1bar$$ and V,T are constant $$wB=2$$ g,$$MB=$$ molar mass of MB $$)$$ Dividing (i) by $$(ii)21=1MA2MB=MB2MA$$, i.e. $$MB=4MA$$

Pressure of 1 gm an ideal gas A at 27°C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature, the pressure becomes 3 bar. Find a relationship between their molecular masses.

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