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Question

Calcium carbide reacts with water to produce acetylene gas according to the following equation:

CaCX2(s)+2HX2O(l)Ca(OH)X2(aq)+CX2HX2(g)\ce{CaC2 (s) + 2H2O (l) -> Ca(OH)2 (aq) + C2H2 (g)}

The product gas, CX2HX2\ce{C2H2} is collected over water at a temperature of 25°C25\degree\ce C and a pressure of 750 mmHg750\text{ mmHg}. If the wet CX2HX2\ce{C2H2} gas formed occupies a volume of 7.52L7.52\ce L, the number of moles of CaCX2\ce{CaC2} reacted was _____ mol. The vapor pressure of water is 23.8 mmHg23.8\text{ mmHg} at 25°C25\degree\ce C.

Solution

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Two important concepts in chemistry are highlighted in this problem: Ideal Gas Law and Dalton's Law of Partial Pressure. The Ideal Gas Law defines the relationship of pressure, volume, temperature, and the number of gaseous moles in one formula as a combination of the four gas laws: Boyle's Law, Charles' Law, Gay-Lussac's Law, and Avogadro's Law. The formula is:

PV=nRTPV=nRT

where PP is the pressure, VV is the volume, nn is the mole of the gaseous molecule, TT is the absolute temperature, and RR is the ideal gas constant at 0.0821 L atm/ mol K0.0821\text{ L atm/ mol K}.

In addition to this, Dalton's Law of Partial Pressure is highlighted in the problem, which states that the partial pressure of gaseous molecule contributes to the sum total pressure experienced. The formula of Dalton's Law of Partial Pressure is:

Ptotal=PiP_{total}=\sum P_i

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