60 g of CaCO3 is heated in a rigid evacuated…

60 g of CaCO3 is heated in a rigid evacuated 41 L vessel at 1000 K until equilibrium CaCO3(s)rightleftharpoons CaO(s)+CO2(g) with Kp=0.50 atm is…

Single correct option

60\ \mathrm{g}

\mathrm{CaCO_3}

is heated in a rigid evacuated

41\ \mathrm{L}

vessel at

1000\ \mathrm{K}

until equilibrium

\mathrm{CaCO_3(s)\rightleftharpoons CaO(s)+CO_2(g)}

with

K_p=0.50\ \mathrm{atm}

is reached. The vessel volume is then doubled at the same temperature and equilibrium is re-established. The mass of

\mathrm{CaCO_3}

left is (

R=0.082\ \mathrm{L\,atm\,K^{-1}mol^{-1}}

\mathrm{CaCO_3}=100

)

Show answer and solution

Answer: (D) $10\ \mathrm{g}$

For the heterogeneous equilibrium

K_p=p_{\mathrm{CO_2}}=0.50

atm, independent of amounts as long as some solid

\mathrm{CaCO_3}

remains. In

41

n=pV/RT=0.50\times41/(0.082\times1000)=0.25

mol, so

25

g decomposed and

35

g is left. After doubling the volume to

82

L the pressure must still be

0.50

atm:

n=0.50\times82/82=0.50

mol of

\mathrm{CO_2}

, i.e.

50

g of

\mathrm{CaCO_3}

decomposed in total. Since

60>50

, solid remains:

60-50=10

g. (

35

g is the value before expansion.)

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