Now make a more accurate calculation of the pressure inside the container. Take
ID: 878238 • Letter: N
Question
Now make a more accurate calculation of the pressure inside the container. Take into account the volume of solid CaO (density = 3.34 g/mL) in the container, and use the vander Waals equation to calculate the pressure. The vander Waals constants for CO2(g) are: a=3.59 (L2atm)/mol2and b=0.0427 L/mol.
A steel container with a volume of 500. 0 mL is evacuated, and 25.0 g of CaCO3 is added. The container and contents are then heated to 1500 K, causing the CaCO3 to decompose completely, according to the equation CaCO3(s)CaO(s)+CO2(g).
Explanation / Answer
1 CaCO3 --> 1 CaO + 1 CO2
volume of CaO...
25.0g CaCO3 x (1 mol CaCO3 / 100.09g CaCO3) x (1 mol CaO / 1 mol CaCO3) x (56.077g CaO / mol CaO) x (1mL / 3.34g CaO) = 4.194mL
volume of CO2 gas
.. 500.0mL - 4.194mL = 495.81mL
moles of CO2 gas..
25.0g CaCO3 x (1 mol CaCO3 / 100.09g CaCO3) x (1 mol CO2 / 1 mol CaCO3) = 0.2498
then
.. (P + an²/V²) x (V - nb) = nRT
rearranges to
.. P = (nRT/(V-nb)) - (an²/V²)
solving..
P = ((0.2498mol x 0.08206Latm/molK x 1500K) / (0.49581L - 0.2498 mol x .0427L/mol)) - (3.59 L²atm/mol² x (0.2498mol)² / (0.49581L)²) = (30.75 Latm / 0.48514L) - (0.9913atm) = (63.38atm) - (0.9913atm) = 62.5atm
if you want to compare it to the ideal gas law using 500mL..
.. PV = nRT
.. P = nRT/V= 0.2498mol x 0.08206 Latm/molK x 1500K / 0.500L = 61.5atm
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